Animate a pendulum: Difference between revisions
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[[Category:Animation]]
{{task|Temporal media}}
{{requires|Graphics}}
[[File:pendulum.gif|500px||right|Capture of the Oz version.]]
One good way of making an animation is by simulating a physical system and illustrating the variables in that system using a dynamically changing graphical display.
The classic such physical system is a [[wp:Pendulum|simple gravity pendulum]].
;Task:
Create a simple physical model of a pendulum and animate it.
<br><br>
=={{header|Ada}}==
This does not use a GUI, it simply animates the pendulum and prints out the positions. If you want, you can replace the output method with graphical update methods.
X and Y are relative positions of the pendulum to the anchor.
pendulums.ads:
<syntaxhighlight lang="ada">generic
type Float_Type is digits <>;
Gravitation : Float_Type;
package Pendulums is
type Pendulum is private;
function New_Pendulum (Length : Float_Type;
Theta0 : Float_Type) return Pendulum;
function Get_X (From : Pendulum) return Float_Type;
function Get_Y (From : Pendulum) return Float_Type;
procedure Update_Pendulum (Item : in out Pendulum; Time : in Duration);
private
type Pendulum is record
Length : Float_Type;
Theta : Float_Type;
X : Float_Type;
Y : Float_Type;
Velocity : Float_Type;
end record;
end Pendulums;</syntaxhighlight>
pendulums.adb:
<syntaxhighlight lang="ada">with Ada.Numerics.Generic_Elementary_Functions;
package body Pendulums is
package Math is new Ada.Numerics.Generic_Elementary_Functions (Float_Type);
function New_Pendulum (Length : Float_Type;
Theta0 : Float_Type) return Pendulum is
Result : Pendulum;
begin
Result.Length := Length;
Result.Theta := Theta0 / 180.0 * Ada.Numerics.Pi;
Result.X := Math.Sin (Theta0) * Length;
Result.Y := Math.Cos (Theta0) * Length;
Result.Velocity := 0.0;
return Result;
end New_Pendulum;
function Get_X (From : Pendulum) return Float_Type is
begin
return From.X;
end Get_X;
function Get_Y (From : Pendulum) return Float_Type is
begin
return From.Y;
end Get_Y;
procedure Update_Pendulum (Item : in out Pendulum; Time : in Duration) is
Acceleration : constant Float_Type := Gravitation / Item.Length *
Math.Sin (Item.Theta);
begin
Item.X := Math.Sin (Item.Theta) * Item.Length;
Item.Y := Math.Cos (Item.Theta) * Item.Length;
Item.Velocity := Item.Velocity +
Acceleration * Float_Type (Time);
Item.Theta := Item.Theta +
Item.Velocity * Float_Type (Time);
end Update_Pendulum;
end Pendulums;</syntaxhighlight>
example main.adb:
<syntaxhighlight lang="ada">with Ada.Text_IO;
with Ada.Calendar;
with Pendulums;
procedure Main is
package Float_Pendulum is new Pendulums (Float, -9.81);
use Float_Pendulum;
use type Ada.Calendar.Time;
My_Pendulum : Pendulum := New_Pendulum (10.0, 30.0);
Now, Before : Ada.Calendar.Time;
begin
Before := Ada.Calendar.Clock;
loop
Delay 0.1;
Now := Ada.Calendar.Clock;
Update_Pendulum (My_Pendulum, Now - Before);
Before := Now;
-- output positions relative to origin
-- replace with graphical output if wanted
Ada.Text_IO.Put_Line (" X: " & Float'Image (Get_X (My_Pendulum)) &
" Y: " & Float'Image (Get_Y (My_Pendulum)));
end loop;
end Main;</syntaxhighlight>
{{out}}
<pre> X: 5.00000E+00 Y: 8.66025E+00
X: 4.95729E+00 Y: 8.68477E+00
X: 4.87194E+00 Y: 8.73294E+00
X: 4.74396E+00 Y: 8.80312E+00
X: 4.57352E+00 Y: 8.89286E+00
X: 4.36058E+00 Y: 8.99919E+00
X: 4.10657E+00 Y: 9.11790E+00
X: 3.81188E+00 Y: 9.24498E+00
X: 3.47819E+00 Y: 9.37562E+00
X: 3.10714E+00 Y: 9.50504E+00
X: 2.70211E+00 Y: 9.62801E+00
X: 2.26635E+00 Y: 9.73980E+00
X: 1.80411E+00 Y: 9.83591E+00
X: 1.32020E+00 Y: 9.91247E+00
X: 8.20224E-01 Y: 9.96630E+00
X: 3.10107E-01 Y: 9.99519E+00
X: -2.03865E-01 Y: 9.99792E+00
X: -7.15348E-01 Y: 9.97438E+00
X: -1.21816E+00 Y: 9.92553E+00
X: -1.70581E+00 Y: 9.85344E+00
X: -2.17295E+00 Y: 9.76106E+00
X: -2.61452E+00 Y: 9.65216E+00
X: -3.02618E+00 Y: 9.53112E+00
X: -3.40427E+00 Y: 9.40271E+00
X: -3.74591E+00 Y: 9.27190E+00
X: -4.04873E+00 Y: 9.14373E+00
X: -4.31141E+00 Y: 9.02285E+00
X: -4.53271E+00 Y: 8.91373E+00
X: -4.71186E+00 Y: 8.82034E+00
X: -4.84868E+00 Y: 8.74587E+00
X: -4.94297E+00 Y: 8.69293E+00
X: -4.99459E+00 Y: 8.66337E+00
X: -5.00352E+00 Y: 8.65822E+00
...</pre>
=={{header|Amazing Hopper}}==
{{Trans|FreeBASIC}}
<syntaxhighlight lang="text">
#include <flow.h>
#include <flow-term.h>
DEF-MAIN(argv,argc)
SET( Pen, 0 )
LET( Pen := STR-TO-UTF8(CHAR(219)) )
CLR-SCR
HIDE-CURSOR
GOSUB( Animate a Pendulum )
SHOW-CURSOR
END
RUTINES
DEF-FUN( Animate a Pendulum )
MSET( accel, speed, bx, by )
SET( theta, M_PI_2 ) // pi/2 constant --> flow.h
SET( g, 9.81 )
SET( l, 1 )
SET( px, 65 )
SET( py, 7 )
LOOP( Animate All )
LET( bx := ADD( px, MUL( MUL( l, 23 ), SIN(theta) ) ) )
LET( by := SUB( py, MUL( MUL( l, 23 ), COS(theta) ) ) )
CLR-SCR
{px,py,bx,by} GOSUB( LINE )
{bx, by, 3} GOSUB( CIRCLE )
LET( accel := MUL(g, SIN(theta) DIV-INTO(l) DIV-INTO(4) ) )
LET( speed := ADD( speed, DIV(accel, 100) ) )
LET( theta := ADD( theta, speed ) )
LOCATE (1, 62) PRNL("PENDULUM")
LOCATE (2, 55) PRNL("Press any key to quit")
SLEEP( 0.1 )
BACK-IF ( NOT( KEY-PRESSED? ), Animate All )
RET
/* DDA Algorithm */
DEF-FUN(LINE, x1, y1, x2, y2)
MSET( x, y, dx, dy, paso, i, gm )
STOR( SUB(x2, x1) SUB(y2, y1), dx, dy )
LET( paso := IF( GE?( ABS(dx) » (DX), ABS(dy)»(DY) ), DX, DY ) )
// increment:
STOR( DIV(dx, paso) DIV(dy, paso), dx, dy )
// print line:
SET( i, 0 )
WHILE( LE?(i, paso), ++i )
LOCATE( y1, x1 ), PRNL( Pen )
STOR( ADD( x1, dx) ADD( y1, dy ), x1, y1 )
WEND
RET
DEF-FUN( Plot Points, xc, yc ,x1 ,y1 )
LOCATE( ADD(xc,x1), ADD( yc, y1) ), PRN( Pen )
LOCATE( SUB(xc,x1), ADD( yc, y1) ), PRN( Pen )
LOCATE( ADD(xc,x1), SUB( yc, y1) ), PRN( Pen )
LOCATE( SUB(xc,x1), SUB( yc, y1) ), PRN( Pen )
LOCATE( ADD(xc,y1), ADD( yc, x1) ), PRN( Pen )
LOCATE( SUB(xc,y1), ADD( yc, x1) ), PRN( Pen )
LOCATE( ADD(xc,y1), SUB( yc, x1) ), PRN( Pen )
LOCATE( SUB(xc,y1), SUB( yc, x1) ), PRNL( Pen )
RET
DEF-FUN( CIRCLE, xc, yc, ratio )
MSET( x, p )
SET( y, ratio )
LOCATE( yc,xc ), PRNL("O")
{yc, xc, y, x} GOSUB( Plot Points )
LET( p := SUB( 1, ratio ) )
LOOP( Print Circle )
++x
COND( LT?( p, 0 ) )
LET( p := ADD( p, MUL(2,x) ) PLUS(1) )
ELS
--y
LET( p := ADD( p, MUL(2, SUB(x,y))) PLUS(1) )
CEND
{yc, xc, y, x} GOSUB( Plot Points )
BACK-IF-LT( x, y, Print Circle )
RET
</syntaxhighlight>
{{out}}
<pre>
PENDULUM
Press any key to quit
██
██
██
██
█
██
██
██
██ ███
██ █
███ █
█ O █
█ █
█ █
███
</pre>
<pre>
FALSE MODE GRAPHICS.
You can simulate a pseudo graphical mode in an Ubuntu Linux terminal by adding the following lines:
</pre>
<syntaxhighlight lang="amazing hopper">
SYS("gsettings set org.gnome.Terminal.Legacy.Profile:/org/gnome/terminal/legacy/profiles:/:.../ font 'Ubuntu Mono 1'")
CLR-SCR
HIDE-CURSOR
GOSUB( Animate a Pendulum )
SYS("gsettings set org.gnome.Terminal.Legacy.Profile:/org/gnome/terminal/legacy/profiles:/:.../ font 'Ubuntu Mono 12'")
SHOW-CURSOR
</syntaxhighlight>
<pre>
And substituting the holding coordinates of the pendulum:
</pre>
<syntaxhighlight lang="amazing hopper">
// in "Animate a Pendulum"
SET( px, 640 )//65 )
SET( py, 30 ) //7 )
// long of the line:
LET( bx := ADD( px, MUL( MUL( l, 180 ), SIN(theta) ) ) )
LET( by := SUB( py, MUL( MUL( l, 180 ), COS(theta) ) ) )
// and circle ratio:
{bx, by, 10} GOSUB( CIRCLE )
</syntaxhighlight>
=={{header|AutoHotkey}}==
This version doesn't use an complex physics calculation - I found a faster way.
{{libheader|GDIP}}
<syntaxhighlight lang="autohotkey">SetBatchlines,-1
;settings
SizeGUI:={w:650,h:400} ;Guisize
pendulum:={length:300,maxangle:90,speed:2,size:30,center:{x:Sizegui.w//2,y:10}} ;pendulum length, size, center, speed and maxangle
pendulum.maxangle:=pendulum.maxangle*0.01745329252
p_Token:=Gdip_Startup()
Gui,+LastFound
Gui,show,% "w" SizeGUI.w " h" SizeGUI.h
hwnd:=WinActive()
hdc:=GetDC(hwnd)
start:=A_TickCount/1000
G:=Gdip_GraphicsFromHDC(hdc)
pBitmap:=Gdip_CreateBitmap(650, 450)
G2:=Gdip_GraphicsFromImage(pBitmap)
Gdip_SetSmoothingMode(G2, 4)
pBrush := Gdip_BrushCreateSolid(0xff0000FF)
pBrush2 := Gdip_BrushCreateSolid(0xFF777700)
pPen:=Gdip_CreatePenFromBrush(pBrush2, 10)
SetTimer,Update,10
Update:
Gdip_GraphicsClear(G2,0xFFFFFFFF)
time:=start-(A_TickCount/1000*pendulum.speed)
angle:=sin(time)*pendulum.maxangle
x2:=sin(angle)*pendulum.length+pendulum.center.x
y2:=cos(angle)*pendulum.length+pendulum.center.y
Gdip_DrawLine(G2,pPen,pendulum.center.x,pendulum.center.y,x2,y2)
GDIP_DrawCircle(G2,pBrush,pendulum.center.x,pendulum.center.y,15)
GDIP_DrawCircle(G2,pBrush2,x2,y2,pendulum.size)
Gdip_DrawImage(G, pBitmap)
return
GDIP_DrawCircle(g,b,x,y,r){
Gdip_FillEllipse(g, b, x-r//2,y-r//2 , r, r)
}
GuiClose:
ExitApp</syntaxhighlight>
=={{header|BASIC}}==
==={{header|Applesoft BASIC}}===
{{trans|Commodore BASIC}}
Two shapes are used to draw and undraw the pendulum. Undrawing and drawing is done on the page that is not being displayed to make the animation flicker free. Animation code is compacted and hoisted to the beginning of the program. Variables are defined for all non-zero values.
<syntaxhighlight lang="gwbasic"> 0 ON NOT T GOTO 9: FOR Q = 0 TO T STEP 0:BX = PX + L * S * SIN (F):BY = PY - L * S * COS (F): HCOLOR= 0: FOR I = 0 TO N(P): DRAW T + (I = N(P)) AT X(P,I),Y(P,I): NEXT I:N(P) = 0: HCOLOR= C
1 FOR X = PX TO BX STEP (BX - PX) / Z:Y = PY + (X - PX) * (BY - PY) / (BX - PX): DRAW T AT X,Y:X(P,N(P)) = X:Y(P,N(P)) = Y:N(P) = N(P) + 1: NEXT X
2 HCOLOR= T: DRAW B AT BX,BY:X(P,N(P)) = BX:Y(P,N(P)) = BY:A = PEEK (R + P):P = NOT P: POKE U,W + W * P:A = G * SIN (F) / L / H:V = V + A / Z:F = F + V: NEXT Q
9 DIM N(1),X(1,11),Y(1,11): FOR P = 32 TO 64 STEP 32: POKE 230,P: HCOLOR= 0: HPLOT 0,0: CALL 62454: NEXT :R = 49236:P = ( PEEK (R) + PEEK (49234) + PEEK (49239) + PEEK (49232)) * 0 + 1
10 S$ = CHR$ (2) + CHR$ (0) + CHR$ (6) + CHR$ (0) + CHR$ (8) + CHR$ (0) + "-" + CHR$ (0) + ".%'?>..%" + CHR$ (0): PRINT MID$ ( STR$ ( FRE (0)) + S$,1,0);: POKE 236, PEEK (131): POKE 237, PEEK (132)
15 S = PEEK (236) + PEEK (237) * 256: POKE 232, PEEK (S + 1): POKE 233, PEEK (S + 2): SCALE= 1: ROT= 0
20 T = 1
25 F = 3.1415926535 / 2: REM THETA
30 G = 9.81
35 L = 0.5
40 V = 0: REM SPEED
45 PX = 140
50 PY = 80
55 S = 20
60 Z = 10
65 C = 3
70 B = 2
75 U = 230
80 W = 32
85 H = 50
90 GOTO</syntaxhighlight>
==={{header|BBC BASIC}}===
{{works with|BBC BASIC for Windows}}
<syntaxhighlight lang="bbcbasic"> MODE 8
*FLOAT 64
VDU 23,23,4;0;0;0; : REM Set line thickness
theta = RAD(40) : REM initial displacement
g = 9.81 : REM acceleration due to gravity
l = 0.50 : REM length of pendulum in metres
REPEAT
PROCpendulum(theta, l)
WAIT 1
PROCpendulum(theta, l)
accel = - g * SIN(theta) / l / 100
speed += accel / 100
theta += speed
UNTIL FALSE
END
DEF PROCpendulum(a, l)
LOCAL pivotX, pivotY, bobX, bobY
pivotX = 640
pivotY = 800
bobX = pivotX + l * 1000 * SIN(a)
bobY = pivotY - l * 1000 * COS(a)
GCOL 3,6
LINE pivotX, pivotY, bobX, bobY
GCOL 3,11
CIRCLE FILL bobX + 24 * SIN(a), bobY - 24 * COS(a), 24
ENDPROC</syntaxhighlight>
==={{header|Commodore BASIC}}===
<syntaxhighlight lang="commodorebasic">10 GOSUB 1000
20 THETA = π/2
30 G = 9.81
40 L = 0.5
50 SPEED = 0
60 PX = 20
70 PY = 1
80 BX = PX+L*20*SIN(THETA)
90 BY = PY-L*20*COS(THETA)
100 PRINT CHR$(147);
110 FOR X=PX TO BX STEP (BX-PX)/10
120 Y=PY+(X-PX)*(BY-PY)/(BX-PX)
130 PRINT CHR$(19);LEFT$(X$,X);LEFT$(Y$,Y);"."
140 NEXT
150 PRINT CHR$(19);LEFT$(X$,BX);LEFT$(Y$,BY);CHR$(113)
160 ACCEL=G*SIN(THETA)/L/50
170 SPEED=SPEED+ACCEL/10
180 THETA=THETA+SPEED
190 GOTO 80
980 REM ** SETUP STRINGS TO BE USED **
990 REM ** FOR CURSOR POSITIONING **
1000 FOR I=0 TO 39: X$ = X$+CHR$(29): NEXT
1010 FOR I=0 TO 24: Y$ = Y$+CHR$(17): NEXT
1020 RETURN</syntaxhighlight>
==={{header|FreeBASIC}}===
<syntaxhighlight lang="freebasic">Const PI = 3.141592920
Dim As Double theta, g, l, accel, speed, px, py, bx, by
theta = PI/2
g = 9.81
l = 1
speed = 0
px = 320
py = 10
Screen 17 '640x400 graphic
Do
bx=px+l*300*Sin(theta)
by=py-l*300*Cos(theta)
Cls
Line (px,py)-(bx,by)
Circle (bx,by),5,,,,,F
accel=g*Sin(theta)/l/100
speed=speed+accel/100
theta=theta+speed
Draw String (0,370), "Pendulum"
Draw String (0,385), "Press any key to quit"
Sleep 10
Loop Until Inkey()<>""</syntaxhighlight>
==={{header|IS-BASIC}}===
<syntaxhighlight lang="is-basic">100 PROGRAM "Pendulum.bas"
110 LET THETA=RAD(50):LET G=9.81:LET L=.5
120 CALL INIC
130 CALL DRAWING
140 CALL ANIMATE
150 CALL RESET
160 END
170 DEF INIC
180 CLOSE #102
190 OPTION ANGLE RADIANS
200 SET STATUS OFF:SET INTERRUPT STOP OFF:SET BORDER 56
210 SET VIDEO MODE 1:SET VIDEO COLOR 1:SET VIDEO X 14:SET VIDEO Y 8
220 FOR I=1 TO 24
230 OPEN #I:"video:"
240 SET #I:PALETTE 56,0,255,YELLOW
250 NEXT
260 END DEF
270 DEF DRAWING
280 LET SPD=0
290 FOR I=1 TO 24
300 DISPLAY #I:AT 3 FROM 1 TO 8
310 SET #I:INK 2
320 PLOT #I:224,280,ELLIPSE 10,10
330 PLOT #I:0,280;214,280,234,280;446,280
340 SET #I:INK 1
350 CALL PENDULUM(THETA,L,I)
360 LET ACC=-G*SIN(THETA)/L/100
370 LET SPD=SPD+ACC/10.5
380 LET THETA=THETA+SPD
390 NEXT
400 END DEF
410 DEF PENDULUM(A,L,CH)
420 LET PX=224:LET PY=280
430 LET BX=PX+L*460*SIN(A)
440 LET BY=PY-L*460*COS(A)
450 PLOT #CH:PX,PY;BX,BY
460 PLOT #CH:BX+24*SIN(A),BY-24*COS(A),ELLIPSE 20,20,
470 SET #CH:INK 3:PLOT #CH:PAINT
480 END DEF
490 DEF ANIMATE
500 DO
510 FOR I=1 TO 24
520 DISPLAY #I:AT 3 FROM 1 TO 8
530 NEXT
540 FOR I=23 TO 2 STEP-1
550 DISPLAY #I:AT 3 FROM 1 TO 8
560 NEXT
570 LOOP UNTIL INKEY$=CHR$(27)
580 END DEF
590 DEF RESET
600 TEXT 40:SET STATUS ON:SET INTERRUPT STOP ON:SET BORDER 0
610 FOR I=24 TO 1 STEP-1
620 CLOSE #I
630 NEXT
640 END DEF</syntaxhighlight>
=={{header|C}}==
{{libheader|GLUT}}
<syntaxhighlight lang="c">#include <stdlib.h>
#include <math.h>
#include <
#include <
#include <sys/time.h>
#define
#define
double alpha, accl, omega = 0, E;
struct timeval tv;
double elappsed() {
struct timeval now;
gettimeofday(&now, 0);
int ret = (now.tv_sec - tv.tv_sec) * 1000000
+ now.tv_usec - tv.tv_usec;
tv = now;
return ret / 1.e6;
}
void resize(int w, int h)
{
glViewport(0, 0, w, h);
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
glMatrixMode(GL_MODELVIEW);
glLoadIdentity();
glOrtho(0, w, h, 0, -1, 1);
}
void render()
{
resize(640, 320);
glClear(GL_COLOR_BUFFER_BIT);
glBegin(GL_LINES);
glVertex2d(320, 0);
glVertex2d(x, y);
glEnd();
glFlush();
double us = elappsed();
alpha += (omega + us * accl / 2) * us;
omega += accl * us;
/* don't let precision error go out of hand */
if (length * g * (1 - cos(alpha)) >= E) {
alpha = (alpha < 0 ? -1 : 1) * acos(1 - E / length / g);
omega = 0;
}
accl = -g / length * sin(alpha);
}
void
{
glutInit(c, v);
glutInitDisplayMode(GLUT_RGB);
glutInitWindowSize(640, 320);
glutIdleFunc(render);
glutCreateWindow("Pendulum");
}
int main(int c, char **v)
{
alpha = 4 * atan2(1, 1) / 2.1;
E = length * g * (1 - cos(alpha));
accl =
omega = 0;
gettimeofday(&tv, 0);
init_gfx(&c, v);
glutMainLoop();
return 0;
}</syntaxhighlight>
=={{header|C sharp|C#}}==
{{libheader|Windows Forms}}
{{libheader|GDI (System.Drawing)}}
<syntaxhighlight lang="csharp">
using System;
using System.Drawing;
using System.Windows.Forms;
class CSharpPendulum
{
Form _form;
Timer _timer;
double _angle = Math.PI / 2,
_angleAccel,
_angleVelocity = 0,
_dt = 0.1;
int _length = 50;
[STAThread]
static void Main()
{
var p = new CSharpPendulum();
}
public CSharpPendulum()
{
_form = new Form() { Text = "Pendulum", Width = 200, Height = 200 };
_timer = new Timer() { Interval = 30 };
_timer.Tick += delegate(object sender, EventArgs e)
{
int anchorX = (_form.Width / 2) - 12,
anchorY = _form.Height / 4,
ballX = anchorX + (int)(Math.Sin(_angle) * _length),
ballY = anchorY + (int)(Math.Cos(_angle) * _length);
_angleAccel = -9.81 / _length * Math.Sin(_angle);
_angleVelocity += _angleAccel * _dt;
_angle += _angleVelocity * _dt;
Bitmap dblBuffer = new Bitmap(_form.Width, _form.Height);
Graphics g = Graphics.FromImage(dblBuffer);
Graphics f = Graphics.FromHwnd(_form.Handle);
g.DrawLine(Pens.Black, new Point(anchorX, anchorY), new Point(ballX, ballY));
g.FillEllipse(Brushes.Black, anchorX - 3, anchorY - 4, 7, 7);
g.FillEllipse(Brushes.DarkGoldenrod, ballX - 7, ballY - 7, 14, 14);
f.Clear(Color.White);
f.DrawImage(dblBuffer, new Point(0, 0));
};
_timer.Start();
Application.Run(_form);
}
}
</syntaxhighlight>
=={{header|C++}}==
{{libheader|wxWidgets}}
File wxPendulumDlg.hpp
<syntaxhighlight lang="cpp">
#ifndef __wxPendulumDlg_h__
#define __wxPendulumDlg_h__
// ---------------------
/// @author Martin Ettl
/// @date 2013-02-03
// ---------------------
#ifdef __BORLANDC__
#pragma hdrstop
#endif
#ifndef WX_PRECOMP
#include <wx/wx.h>
#include <wx/dialog.h>
#else
#include <wx/wxprec.h>
#endif
#include <wx/timer.h>
#include <wx/dcbuffer.h>
#include <cmath>
class wxPendulumDlgApp : public wxApp
{
public:
bool OnInit();
int OnExit();
};
class wxPendulumDlg : public wxDialog
{
public:
wxPendulumDlg(wxWindow *parent, wxWindowID id = 1, const wxString &title = wxT("wxPendulum"),
const wxPoint& pos = wxDefaultPosition, const wxSize& size = wxDefaultSize,
long style = wxSUNKEN_BORDER | wxCAPTION | wxRESIZE_BORDER | wxSYSTEM_MENU | wxDIALOG_NO_PARENT | wxMINIMIZE_BOX | wxMAXIMIZE_BOX | wxCLOSE_BOX);
virtual ~wxPendulumDlg();
// Event handler
void wxPendulumDlgPaint(wxPaintEvent& event);
void wxPendulumDlgSize(wxSizeEvent& event);
void OnTimer(wxTimerEvent& event);
private:
// a pointer to a timer object
wxTimer *m_timer;
unsigned int m_uiLength;
double m_Angle;
double m_AngleVelocity;
enum wxIDs
{
ID_WXTIMER1 = 1001,
ID_DUMMY_VALUE_
};
void OnClose(wxCloseEvent& event);
void CreateGUIControls();
DECLARE_EVENT_TABLE()
};
#endif // __wxPendulumDlg_h__
</syntaxhighlight>
File wxPendulumDlg.cpp
<syntaxhighlight lang="cpp">
// ---------------------
/// @author Martin Ettl
/// @date 2013-02-03
// ---------------------
#include "wxPendulumDlg.hpp"
#include <wx/pen.h>
IMPLEMENT_APP(wxPendulumDlgApp)
bool wxPendulumDlgApp::OnInit()
{
wxPendulumDlg* dialog = new wxPendulumDlg(NULL);
SetTopWindow(dialog);
dialog->Show(true);
return true;
}
int wxPendulumDlgApp::OnExit()
{
return 0;
}
BEGIN_EVENT_TABLE(wxPendulumDlg, wxDialog)
EVT_CLOSE(wxPendulumDlg::OnClose)
EVT_SIZE(wxPendulumDlg::wxPendulumDlgSize)
EVT_PAINT(wxPendulumDlg::wxPendulumDlgPaint)
EVT_TIMER(ID_WXTIMER1, wxPendulumDlg::OnTimer)
END_EVENT_TABLE()
wxPendulumDlg::wxPendulumDlg(wxWindow *parent, wxWindowID id, const wxString &title, const wxPoint &position, const wxSize& size, long style)
: wxDialog(parent, id, title, position, size, style)
{
CreateGUIControls();
}
wxPendulumDlg::~wxPendulumDlg()
{
}
void wxPendulumDlg::CreateGUIControls()
{
SetIcon(wxNullIcon);
SetSize(8, 8, 509, 412);
Center();
m_uiLength = 200;
m_Angle = M_PI/2.;
m_AngleVelocity = 0;
m_timer = new wxTimer();
m_timer->SetOwner(this, ID_WXTIMER1);
m_timer->Start(20);
}
void wxPendulumDlg::OnClose(wxCloseEvent& WXUNUSED(event))
{
Destroy();
}
void wxPendulumDlg::wxPendulumDlgPaint(wxPaintEvent& WXUNUSED(event))
{
SetBackgroundStyle(wxBG_STYLE_CUSTOM);
wxBufferedPaintDC dc(this);
// Get window dimensions
wxSize sz = GetClientSize();
// determine the center of the canvas
const wxPoint center(wxPoint(sz.x / 2, sz.y / 2));
// create background color
wxColour powderblue = wxColour(176,224,230);
// draw powderblue background
dc.SetPen(powderblue);
dc.SetBrush(powderblue);
dc.DrawRectangle(0, 0, sz.x, sz.y);
// draw lines
wxPen Pen(*wxBLACK_PEN);
Pen.SetWidth(1);
dc.SetPen(Pen);
dc.SetBrush(*wxBLACK_BRUSH);
double angleAccel, dt = 0.15;
angleAccel = (-9.81 / m_uiLength) * sin(m_Angle);
m_AngleVelocity += angleAccel * dt;
m_Angle += m_AngleVelocity * dt;
int anchorX = sz.x / 2, anchorY = sz.y / 4;
int ballX = anchorX + (int)(sin(m_Angle) * m_uiLength);
int ballY = anchorY + (int)(cos(m_Angle) * m_uiLength);
dc.DrawLine(anchorX, anchorY, ballX, ballY);
dc.SetBrush(*wxGREY_BRUSH);
dc.DrawEllipse(anchorX - 3, anchorY - 4, 7, 7);
dc.SetBrush(wxColour(255,255,0)); // yellow
dc.DrawEllipse(ballX - 7, ballY - 7, 20, 20);
}
void wxPendulumDlg::wxPendulumDlgSize(wxSizeEvent& WXUNUSED(event))
{
Refresh();
}
void wxPendulumDlg::OnTimer(wxTimerEvent& WXUNUSED(event))
{
// force refresh
Refresh();
}
</syntaxhighlight>
This program is tested with wxWidgets version 2.8 and 2.9.
The whole project, including makefile for compiling on Linux
can be download from [https://github.com/orbitcowboy/wxPendulum github].
[[File:WxPendulumScreenshot.png]]
=={{header|Clojure}}==
Clojure solution using an atom and a separate rendering thread
{{libheader|Swing}} {{libheader|AWT}}
<syntaxhighlight lang="clojure">
(ns pendulum
(:import
(javax.swing JFrame)
(java.awt Canvas Graphics Color)))
(def length 200)
(def width (* 2 (+ 50 length)))
(def height (* 3 (/ length 2)))
(def dt 0.1)
(def g 9.812)
(def k (- (/ g length)))
(def anchor-x (/ width 2))
(def anchor-y (/ height 8))
(def angle (atom (/ (Math/PI) 2)))
(defn draw [#^Canvas canvas angle]
(let [buffer (.getBufferStrategy canvas)
g (.getDrawGraphics buffer)
ball-x (+ anchor-x (* (Math/sin angle) length))
ball-y (+ anchor-y (* (Math/cos angle) length))]
(try
(doto g
(.setColor Color/BLACK)
(.fillRect 0 0 width height)
(.setColor Color/RED)
(.drawLine anchor-x anchor-y ball-x ball-y)
(.setColor Color/YELLOW)
(.fillOval (- anchor-x 3) (- anchor-y 4) 7 7)
(.fillOval (- ball-x 7) (- ball-y 7) 14 14))
(finally (.dispose g)))
(if-not (.contentsLost buffer)
(.show buffer)) ))
(defn start-renderer [canvas]
(->>
(fn [] (draw canvas @angle) (recur))
(new Thread)
(.start)))
(defn -main [& args]
(let [frame (JFrame. "Pendulum")
canvas (Canvas.)]
(doto frame
(.setSize width height)
(.setDefaultCloseOperation JFrame/EXIT_ON_CLOSE)
(.setResizable false)
(.add canvas)
(.setVisible true))
(doto canvas
(.createBufferStrategy 2)
(.setVisible true)
(.requestFocus))
(start-renderer canvas)
(loop [v 0]
(swap! angle #(+ % (* v dt)))
(Thread/sleep 15)
(recur (+ v (* k (Math/sin @angle) dt)))) ))
(-main)
</syntaxhighlight>
=={{header|Common Lisp}}==
An approach using closures. Physics code adapted from [[Animate_a_pendulum#Ada|Ada]].
{{libheader|Lispbuilder-SDL}}
Pressing the spacebar adds a pendulum.
<syntaxhighlight lang="lisp">(defvar *frame-rate* 30)
(defvar *damping* 0.99 "Deceleration factor.")
(defun make-pendulum (length theta0 x)
"Returns an anonymous function with enclosed state representing a pendulum."
(let* ((theta (* (/ theta0 180) pi))
(acceleration 0))
(if (< length 40) (setf length 40)) ;;avoid a divide-by-zero
(lambda ()
;;Draws the pendulum, updating its location and speed.
(sdl:draw-line (sdl:point :x x :y 1)
(sdl:point :x (+ (* (sin theta) length) x)
:y (* (cos theta) length)))
(sdl:draw-filled-circle (sdl:point :x (+ (* (sin theta) length) x)
:y (* (cos theta) length))
20
:color sdl:*yellow*
:stroke-color sdl:*white*)
;;The magic constant approximates the speed we want for a given frame-rate.
(incf acceleration (* (sin theta) (* *frame-rate* -0.001)))
(incf theta acceleration)
(setf acceleration (* acceleration *damping*)))))
(defun main (&optional (w 640) (h 480))
(sdl:with-init ()
(sdl:window w h :title-caption "Pendulums"
:fps (make-instance 'sdl:fps-fixed))
(setf (sdl:frame-rate) *frame-rate*)
(let ((pendulums nil))
(sdl:with-events ()
(:quit-event () t)
(:idle ()
(sdl:clear-display sdl:*black*)
(mapcar #'funcall pendulums) ;;Draw all the pendulums
(sdl:update-display))
(:key-down-event (:key key)
(cond ((sdl:key= key :sdl-key-escape)
(sdl:push-quit-event))
((sdl:key= key :sdl-key-space)
(push (make-pendulum (random (- h 100))
(random 90)
(round w 2))
pendulums))))))))</syntaxhighlight>
=={{header|Delphi}}==
{{libheader| Vcl.Forms}}
{{libheader| Vcl.Graphics}}
{{libheader| Vcl.ExtCtrls}}
{{Trans|C#}}
<syntaxhighlight lang="delphi">
unit main;
interface
uses
Vcl.Forms, Vcl.Graphics, Vcl.ExtCtrls;
type
TForm1 = class(TForm)
procedure FormCreate(Sender: TObject);
procedure FormDestroy(Sender: TObject);
private
Timer: TTimer;
angle, angleAccel, angleVelocity, dt: double;
len: Integer;
procedure Tick(Sender: TObject);
end;
var
Form1: TForm1;
implementation
{$R *.dfm}
procedure TForm1.FormCreate(Sender: TObject);
begin
Width := 200;
Height := 200;
DoubleBuffered := True;
Timer := TTimer.Create(nil);
Timer.Interval := 30;
Timer.OnTimer := Tick;
Caption := 'Pendulum';
// initialize
angle := PI / 2;
angleAccel := 0;
angleVelocity := 0;
dt := 0.1;
len := 50;
end;
procedure TForm1.FormDestroy(Sender: TObject);
begin
Timer.Free;
end;
procedure TForm1.Tick(Sender: TObject);
const
HalfPivot = 4;
HalfBall = 7;
var
anchorX, anchorY, ballX, ballY: Integer;
begin
anchorX := Width div 2 - 12;
anchorY := Height div 4;
ballX := anchorX + Trunc(Sin(angle) * len);
ballY := anchorY + Trunc(Cos(angle) * len);
angleAccel := -9.81 / len * Sin(angle);
angleVelocity := angleVelocity + angleAccel * dt;
angle := angle + angleVelocity * dt;
with canvas do
begin
Pen.Color := clBlack;
with Brush do
begin
Style := bsSolid;
Color := clWhite;
end;
FillRect(ClientRect);
MoveTo(anchorX, anchorY);
LineTo(ballX, ballY);
Brush.Color := clGray;
Ellipse(anchorX - HalfPivot, anchorY - HalfPivot, anchorX + HalfPivot,
anchorY + HalfPivot);
Brush.Color := clYellow;
Ellipse(ballX - HalfBall, ballY - HalfBall, ballX + HalfBall, ballY + HalfBall);
end;
end;
end.</syntaxhighlight>
=={{header|E}}==
{{works with|E-on-Java}} (Uses Java Swing for GUI. The animation logic is independent, however.)
The angle <math>\theta</math> of a pendulum with length <math>L</math> and acceleration due to gravity <math>g</math> with all its mass at the end and no friction/air resistance has an acceleration at any given moment of
:<math>\frac{d^
This simulation uses this formula directly, updating the velocity from the acceleration and the position from the velocity; inaccuracy results from the finite timestep.
The event flow works like this:
The ''clock'' object created by the simulation steps the simulation on the specified in the interval.
The simulation writes its output to <code><var>angle</var></code>, which is a ''Lamport slot'' which can notify of updates.
The ''whenever'' set up by <code>makeDisplayComponent</code> listens for updates and triggers redrawing as long as ''interest'' has been expressed, which is done whenever the component actually redraws, which happens only if the component's window is still on screen.
When the window is closed, additionally, the simulation itself is stopped and the application allowed to exit.
(This logic is more general than necessary; it is designed to be suitable for a larger application as well.)
<
pragma.syntax("0.9")
Line 240 ⟶ 1,156:
}
interp.blockAtTop()</
=={{header|EasyLang}}==
[https://easylang.online/apps/pendulum.html Run it]
<syntaxhighlight lang="text">ang = 45
on animate
clear
move 50 50
circle 1
x = 50 + 40 * sin ang
y = 50 + 40 * cos ang
line x y
circle 6
vel += sin ang / 5
ang += vel
.
</syntaxhighlight>
=={{header|Elm}}==
<syntaxhighlight lang="elm">import Color exposing (..)
import Collage exposing (..)
import Element exposing (..)
import Html exposing (..)
import Time exposing (..)
import Html.App exposing (program)
dt = 0.01
scale = 100
type alias Model =
{ angle : Float
, angVel : Float
, length : Float
, gravity : Float
}
type Msg
= Tick Time
init : (Model,Cmd Msg)
init =
( { angle = 3 * pi / 4
, angVel = 0.0
, length = 2
, gravity = -9.81
}
, Cmd.none)
update : Msg -> Model -> (Model, Cmd Msg)
update _ model =
let
angAcc = -1.0 * (model.gravity / model.length) * sin (model.angle)
angVel' = model.angVel + angAcc * dt
angle' = model.angle + angVel' * dt
in
( { model
| angle = angle'
, angVel = angVel'
}
, Cmd.none )
view : Model -> Html Msg
view model =
let
endPoint = ( 0, scale * model.length )
pendulum =
group
[ segment ( 0, 0 ) endPoint
|> traced { defaultLine | width = 2, color = red }
, circle 8
|> filled blue
, ngon 3 10
|> filled green
|> rotate (pi/2)
|> move endPoint
]
in
toHtml <|
collage 700 500
[ pendulum |> rotate model.angle ]
subscriptions : Model -> Sub Msg
subscriptions _ =
Time.every (dt * second) Tick
main =
program
{ init = init
, view = view
, update = update
, subscriptions = subscriptions
}</syntaxhighlight>
Link to live demo: http://dc25.github.io/animatedPendulumElm
=={{header|ERRE}}==
<syntaxhighlight lang="erre">
PROGRAM PENDULUM
!
! for rosettacode.org
!
!$KEY
!$INCLUDE="PC.LIB"
PROCEDURE PENDULUM(A,L)
PIVOTX=320
PIVOTY=0
BOBX=PIVOTX+L*500*SIN(a)
BOBY=PIVOTY+L*500*COS(a)
LINE(PIVOTX,PIVOTY,BOBX,BOBY,6,FALSE)
CIRCLE(BOBX+24*SIN(A),BOBY+24*COS(A),27,11)
PAUSE(0.01)
LINE(PIVOTX,PIVOTY,BOBX,BOBY,0,FALSE)
CIRCLE(BOBX+24*SIN(A),BOBY+24*COS(A),27,0)
END PROCEDURE
BEGIN
SCREEN(9)
THETA=40*p/180 ! initial displacement
G=9.81 ! acceleration due to gravity
L=0.5 ! length of pendulum in metres
LINE(0,0,639,0,5,FALSE)
LOOP
PENDULUM(THETA,L)
ACCEL=-G*SIN(THETA)/L/100
SPEED=SPEED+ACCEL/100
THETA=THETA+SPEED
END LOOP
END PROGRAM
</syntaxhighlight>
PC version: Ctrl+Break to stop.
=={{header|Euler Math Toolbox}}==
Euler Math Toolbox can determine the exact period of a physical pendulum. The result is then used to animate the pendulum. The following code is ready to be pasted back into Euler notebooks.
<pre>
>g=gearth$; l=1m;
>function f(x,y) := [y[2],-g*sin(y[1])/l]
>function h(a) := ode("f",linspace(0,a,100),[0,2])[1,-1]
>period=solve("h",2)
2.06071780729
>t=linspace(0,period,30); s=ode("f",t,[0,2])[1];
>function anim (t,s) ...
$ setplot(-1,1,-1,1);
$ markerstyle("o#");
$ repeat
$ for i=1 to cols(t)-1;
$ clg;
$ hold on;
$ plot([0,sin(s[i])],[1,1-cos(s[i])]);
$ mark([0,sin(s[i])],[1,1-cos(s[i])]);
$ hold off;
$ wait(t[i+1]-t[i]);
$ end;
$ until testkey();
$ end
$endfunction
>anim(t,s);
>
</pre>
=={{header|Euphoria}}==
===DOS32 version===
{{works with|Euphoria|3.1.1}}
<syntaxhighlight lang="euphoria">include graphics.e
include misc.e
constant dt = 1E-3
constant g = 50
sequence vc
sequence suspension
atom len
procedure draw_pendulum(atom color, atom len, atom alfa)
sequence point
point = (len*{sin(alfa),cos(alfa)} + suspension)
draw_line(color, {suspension, point})
ellipse(color,0,point-{10,10},point+{10,10})
end procedure
function wait()
atom t0
t0 = time()
while time() = t0 do
if get_key() != -1 then
return 1
end if
end while
return 0
end function
procedure animation()
atom alfa, omega, epsilon
if graphics_mode(18) then
end if
vc = video_config()
suspension = {vc[VC_XPIXELS]/2,vc[VC_YPIXELS]/2}
len = vc[VC_YPIXELS]/2-20
alfa = PI/2
omega = 0
while 1 do
draw_pendulum(BRIGHT_WHITE,len,alfa)
if wait() then
exit
end if
draw_pendulum(BLACK,len,alfa)
epsilon = -len*sin(alfa)*g
omega += dt*epsilon
alfa += dt*omega
end while
if graphics_mode(-1) then
end if
end procedure
animation()</syntaxhighlight>
=={{header|F_Sharp|F#}}==
A nice application of F#'s support for units of measure.
<syntaxhighlight lang="fsharp">open System
open System.Drawing
open System.Windows.Forms
// define units of measurement
[<Measure>] type m; // metres
[<Measure>] type s; // seconds
// a pendulum is represented as a record of physical quantities
type Pendulum =
{ length : float<m>
gravity : float<m/s^2>
velocity : float<m/s>
angle : float
}
// calculate the next state of a pendulum
let next pendulum deltaT : Pendulum =
let k = -pendulum.gravity / pendulum.length
let acceleration = k * Math.Sin pendulum.angle * 1.0<m>
let newVelocity = pendulum.velocity + acceleration * deltaT
let newAngle = pendulum.angle + newVelocity * deltaT / 1.0<m>
{ pendulum with velocity = newVelocity; angle = newAngle }
// paint a pendulum (using hard-coded screen coordinates)
let paint pendulum (gr: System.Drawing.Graphics) =
let homeX = 160
let homeY = 50
let length = 140.0
// draw plate
gr.DrawLine( new Pen(Brushes.Gray, width=2.0f), 0, homeY, 320, homeY )
// draw pivot
gr.FillEllipse( Brushes.Gray, homeX-5, homeY-5, 10, 10 )
gr.DrawEllipse( new Pen(Brushes.Black), homeX-5, homeY-5, 10, 10 )
// draw the pendulum itself
let x = homeX + int( length * Math.Sin pendulum.angle )
let y = homeY + int( length * Math.Cos pendulum.angle )
// draw rod
gr.DrawLine( new Pen(Brushes.Black, width=3.0f), homeX, homeY, x, y )
// draw bob
gr.FillEllipse( Brushes.Yellow, x-15, y-15, 30, 30 )
gr.DrawEllipse( new Pen(Brushes.Black), x-15, y-15, 30, 30 )
// defines an operator "-?" that calculates the time from t2 to t1
// where t2 is optional
let (-?) (t1: DateTime) (t2: DateTime option) : float<s> =
match t2 with
| None -> 0.0<s> // only one timepoint given -> difference is 0
| Some t -> (t1 - t).TotalSeconds * 1.0<s>
// our main window is double-buffered form that reacts to paint events
type PendulumForm() as self =
inherit Form(Width=325, Height=240, Text="Pendulum")
let mutable pendulum = { length = 1.0<m>;
gravity = 9.81<m/s^2>
velocity = 0.0<m/s>
angle = Math.PI / 2.0
}
let mutable lastPaintedAt = None
let updateFreq = 0.01<s>
do self.DoubleBuffered <- true
self.Paint.Add( fun args ->
let now = DateTime.Now
let deltaT = now -? lastPaintedAt |> min 0.01<s>
lastPaintedAt <- Some now
pendulum <- next pendulum deltaT
let gr = args.Graphics
gr.Clear( Color.LightGray )
paint pendulum gr
// initiate a new paint event after a while (non-blocking)
async { do! Async.Sleep( int( 1000.0 * updateFreq / 1.0<s> ) )
self.Invalidate()
}
|> Async.Start
)
[<STAThread>]
Application.Run( new PendulumForm( Visible=true ) )</syntaxhighlight>
=={{header|Factor}}==
Approximation of the pendulum for small swings : theta = theta0 * cos(omega0 * t)
<syntaxhighlight lang="factor">USING: accessors alarms arrays calendar colors.constants kernel
locals math math.constants math.functions math.rectangles
math.vectors opengl sequences system ui ui.gadgets ui.render ;
IN: pendulum
CONSTANT: g 9.81
CONSTANT: l 20
CONSTANT: theta0 0.5
: current-time ( -- time ) nano-count -9 10^ * ;
: T0 ( -- T0 ) 2 pi l g / sqrt * * ;
: omega0 ( -- omega0 ) 2 pi * T0 / ;
: theta ( -- theta ) current-time omega0 * cos theta0 * ;
: relative-xy ( theta l -- xy )
swap [ sin * ] [ cos * ] 2bi 2array ;
: theta-to-xy ( origin theta l -- xy ) relative-xy v+ ;
TUPLE: pendulum-gadget < gadget alarm ;
: O ( gadget -- origin ) rect-bounds [ drop ] [ first 2 / ] bi* 0 2array ;
: window-l ( gadget -- l ) rect-bounds [ drop ] [ second ] bi* ;
: gadget-xy ( gadget -- xy ) [ O ] [ drop theta ] [ window-l ] tri theta-to-xy ;
M: pendulum-gadget draw-gadget*
COLOR: black gl-color
[ O ] [ gadget-xy ] bi gl-line ;
M:: pendulum-gadget graft* ( gadget -- )
[ gadget relayout-1 ]
20 milliseconds every gadget (>>alarm) ;
M: pendulum-gadget ungraft* alarm>> cancel-alarm ;
: <pendulum-gadget> ( -- gadget )
pendulum-gadget new
{ 500 500 } >>pref-dim ;
: pendulum-main ( -- )
[ <pendulum-gadget> "pendulum" open-window ] with-ui ;
MAIN: pendulum-main
</syntaxhighlight>
=={{header|FBSL}}==
<syntaxhighlight lang="qbasic">#INCLUDE <Include\Windows.inc>
FBSLSETTEXT(ME, "Pendulum")
FBSL.SETTIMER(ME, 1000, 10)
RESIZE(ME, 0, 0, 300, 200)
CENTER(ME)
SHOW(ME)
BEGIN EVENTS
SELECT CASE CBMSG
CASE WM_TIMER
' Request redraw
InvalidateRect(ME, NULL, FALSE)
RETURN 0
CASE WM_PAINT
Swing()
CASE WM_CLOSE
FBSL.KILLTIMER(ME, 1000)
END SELECT
END EVENTS
SUB Swing()
TYPE RECT: %rcLeft, %rcTop, %rcRight, %rcBottom: END TYPE
STATIC rc AS RECT, !!acceleration, !!velocity, !!angle = M_PI_2, %pendulum = 100
GetClientRect(ME, @rc)
' Recalculate
DIM headX = rc.rcRight / 2, headY = rc.rcBottom / 4
DIM tailX = headX + SIN(angle) * pendulum
DIM tailY = headY + COS(angle) * pendulum
acceleration = -9.81 / pendulum * SIN(angle)
INCR(velocity, acceleration * 0.1)(angle, velocity * 0.1)
' Create backbuffer
CreateCompatibleDC(GetDC(ME))
SelectObject(CreateCompatibleDC, CreateCompatibleBitmap(GetDC, rc.rcRight, rc.rcBottom))
' Draw to backbuffer
FILLSTYLE(FILL_SOLID): FILLCOLOR(RGB(200, 200, 0))
LINE(CreateCompatibleDC, 0, 0, rc.rcRight, rc.rcBottom, GetSysColor(COLOR_BTNHILIGHT), TRUE, TRUE)
LINE(CreateCompatibleDC, 0, headY, rc.rcRight, headY, GetSysColor(COLOR_3DSHADOW))
DRAWWIDTH(3)
LINE(CreateCompatibleDC, headX, headY, tailX, tailY, RGB(200, 0, 0))
DRAWWIDTH(1)
CIRCLE(CreateCompatibleDC, headX, headY, 2, GetSysColor, 0, 360, 1, TRUE)
CIRCLE(CreateCompatibleDC, tailX, tailY, 10, GetSysColor, 0, 360, 1, FALSE)
' Blit to window
BitBlt(GetDC, 0, 0, rc.rcRight, rc.rcBottom, CreateCompatibleDC, 0, 0, SRCCOPY)
ReleaseDC(ME, GetDC)
' Delete backbuffer
DeleteObject(SelectObject(CreateCompatibleDC, SelectObject))
DeleteDC(CreateCompatibleDC)
END SUB</syntaxhighlight>
'''Screenshot:'''
[[File:FBSLPendulum.png]]
=={{header|Fortran}}==
Uses system commands (gfortran) to clear the screen. An initial starting angle is allowed between 90 (to the right) and -90 degrees (to the left). It checks for incorrect inputs.
<syntaxhighlight lang="fortran">
!Implemented by Anant Dixit (October, 2014)
program animated_pendulum
implicit none
double precision, parameter :: pi = 4.0D0*atan(1.0D0), l = 1.0D-1, dt = 1.0D-2, g = 9.8D0
integer :: io
double precision :: s_ang, c_ang, p_ang, n_ang
write(*,*) 'Enter starting angle (in degrees):'
do
read(*,*,iostat=io) s_ang
if(io.ne.0 .or. s_ang.lt.-90.0D0 .or. s_ang.gt.90.0D0) then
write(*,*) 'Please enter an angle between 90 and -90 degrees:'
else
exit
end if
end do
call execute_command_line('cls')
c_ang = s_ang*pi/180.0D0
p_ang = c_ang
call display(c_ang)
do
call next_time_step(c_ang,p_ang,g,l,dt,n_ang)
if(abs(c_ang-p_ang).ge.0.05D0) then
call execute_command_line('cls')
call display(c_ang)
end if
end do
end program
subroutine next_time_step(c_ang,p_ang,g,l,dt,n_ang)
double precision :: c_ang, p_ang, g, l, dt, n_ang
n_ang = (-g*sin(c_ang)/l)*2.0D0*dt**2 + 2.0D0*c_ang - p_ang
p_ang = c_ang
c_ang = n_ang
end subroutine
subroutine display(c_ang)
double precision :: c_ang
character (len=*), parameter :: cfmt = '(A1)'
double precision :: rx, ry
integer :: x, y, i, j
rx = 45.0D0*sin(c_ang)
ry = 22.5D0*cos(c_ang)
x = int(rx)+51
y = int(ry)+2
do i = 1,32
do j = 1,100
if(i.eq.y .and. j.eq.x) then
write(*,cfmt,advance='no') 'O'
else if(i.eq.y .and. (j.eq.(x-1).or.j.eq.(x+1))) then
write(*,cfmt,advance='no') 'G'
else if(j.eq.x .and. (i.eq.(y-1).or.i.eq.(y+1))) then
write(*,cfmt,advance='no') 'G'
else if(i.eq.y .and. (j.eq.(x-2).or.j.eq.(x+2))) then
write(*,cfmt,advance='no') '#'
else if(j.eq.x .and. (i.eq.(y-2).or.i.eq.(y+2))) then
write(*,cfmt,advance='no') 'G'
else if((i.eq.(y+1).and.j.eq.(x+1)) .or. (i.eq.(y-1).and.j.eq.(x-1))) then
write(*,cfmt,advance='no') '#'
else if((i.eq.(y+1).and.j.eq.(x-1)) .or. (i.eq.(y-1).and.j.eq.(x+1))) then
write(*,cfmt,advance='no') '#'
else if(j.eq.50) then
write(*,cfmt,advance='no') '|'
else if(i.eq.2) then
write(*,cfmt,advance='no') '-'
else
write(*,cfmt,advance='no') ' '
end if
end do
write(*,*)
end do
end subroutine
</syntaxhighlight>
A small preview (truncated to a few steps of the pendulum changing direction). Initial angle provided = 80 degrees.
<pre>
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</pre>
=={{header|Groovy}}==
Straight translation of Java solution groovified by removing explicit definitions and converting casts to Groovy as style where needed.
<syntaxhighlight lang="groovy">
import java.awt.*;
import javax.swing.*;
class Pendulum extends JPanel implements Runnable {
private angle = Math.PI / 2;
private length;
Pendulum(length) {
this.length = length;
setDoubleBuffered(true);
}
@Override
void paint(Graphics g) {
g.setColor(Color.WHITE);
g.fillRect(0, 0, getWidth(), getHeight());
g.setColor(Color.BLACK);
int anchorX = getWidth() / 2, anchorY = getHeight() / 4;
def ballX = anchorX + (Math.sin(angle) * length) as int;
def ballY = anchorY + (Math.cos(angle) * length) as int;
g.drawLine(anchorX, anchorY, ballX, ballY);
g.fillOval(anchorX - 3, anchorY - 4, 7, 7);
g.fillOval(ballX - 7, ballY - 7, 14, 14);
}
void run() {
def angleAccel, angleVelocity = 0, dt = 0.1;
while (true) {
angleAccel = -9.81 / length * Math.sin(angle);
angleVelocity += angleAccel * dt;
angle += angleVelocity * dt;
repaint();
try { Thread.sleep(15); } catch (InterruptedException ex) {}
}
}
@Override
Dimension getPreferredSize() {
return new Dimension(2 * length + 50, (length / 2 * 3) as int);
}
static void main(String[] args) {
def f = new JFrame("Pendulum");
def p = new Pendulum(200);
f.add(p);
f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
f.pack();
f.setVisible(true);
new Thread(p).start();
}
}
</syntaxhighlight>
=={{header|FutureBasic}}==
<syntaxhighlight lang="futurebasic">
void local fn BuildWindow
window 1, @"Animated Pendulum in FutureBasic", ( 0, 0, 640, 400 )
WindowSetBackgroundColor( 1, fn ColorBlack )
WindowSetMinSize( 1, fn CGSizeMake( 640, 400 ) )
WindowSetMaxSize( 1, fn CGSizeMake( 640, 400 ) )
end fn
local fn AnimatedPendulum
block double theta, gravity, length, accel, speed, weight, tempo, px, py, bx, by
block ColorRef color = fn ColorWithRGB( 0.164, 0.793, 0.075, 1.0 )
theta = pi/2.0 // Denominator of 2.0 = 180-degree swing, < 2.0 narrows inscribed arc, > 2.0 widens it.
gravity = 9.90 // Adjusts effect of gravity on swing. Smaller values slow arc swing.
length = 0.95 // Tweak for length of pendulum arm
speed = 0 // Zero this or you get a propellor!
px = 320 // Pivot horizontal center x point (half window width)
py = 30 // Pivot y center y point from top
weight = 42 // Diameter of pendulum weight
tempo = 75 // Smaller value increases pendulum tempo, larger value slows it.
timerbegin, 0.02, YES
bx = px + length * 300 * sin(theta) // Pendulum bottom x point
by = py - length * 300 * cos(theta) // Pendulum bottom y point
cls
pen 6.0, color
line px, py to bx, by
oval fill bx -weight/2, by -weight/2, weight, weight, color // Traveling weight
pen 4.0
oval fill 313, 20, 16, 16, fn ColorGray // Top center point
accel = gravity * sin(theta) / length / tempo
speed += accel / tempo
theta += speed
timerEnd
end fn
void local fn DoDialog( ev as long, tag as long, wnd as long )
select ( ev )
case _windowWillClose : end
end select
end fn
on dialog fn DoDialog
fn BuildWindow
fn AnimatedPendulum
HandleEvents
</syntaxhighlight>
[[File:Animated_Pendulum_FutureBasic2.gif]]
=={{header|Go}}==
Using {{libheader|GXUI}} from [https://github.com/google/gxui Github]
<syntaxhighlight lang="go">package main
import (
"github.com/google/gxui"
"github.com/google/gxui/drivers/gl"
"github.com/google/gxui/math"
"github.com/google/gxui/themes/dark"
omath "math"
"time"
)
//Two pendulums animated
//Top: Mathematical pendulum with small-angle approxmiation (not appropiate with PHI_ZERO=pi/2)
//Bottom: Simulated with differential equation phi'' = g/l * sin(phi)
const (
ANIMATION_WIDTH int = 480
ANIMATION_HEIGHT int = 320
BALL_RADIUS float32 = 25.0
METER_PER_PIXEL float64 = 1.0 / 20.0
PHI_ZERO float64 = omath.Pi * 0.5
)
var (
l float64 = float64(ANIMATION_HEIGHT) * 0.5
freq float64 = omath.Sqrt(9.81 / (l * METER_PER_PIXEL))
)
type Pendulum interface {
GetPhi() float64
}
type mathematicalPendulum struct {
start time.Time
}
func (p *mathematicalPendulum) GetPhi() float64 {
if (p.start == time.Time{}) {
p.start = time.Now()
}
t := float64(time.Since(p.start).Nanoseconds()) / omath.Pow10(9)
return PHI_ZERO * omath.Cos(t*freq)
}
type numericalPendulum struct {
currentPhi float64
angAcc float64
angVel float64
lastTime time.Time
}
func (p *numericalPendulum) GetPhi() float64 {
dt := 0.0
if (p.lastTime != time.Time{}) {
dt = float64(time.Since(p.lastTime).Nanoseconds()) / omath.Pow10(9)
}
p.lastTime = time.Now()
p.angAcc = -9.81 / (float64(l) * METER_PER_PIXEL) * omath.Sin(p.currentPhi)
p.angVel += p.angAcc * dt
p.currentPhi += p.angVel * dt
return p.currentPhi
}
func draw(p Pendulum, canvas gxui.Canvas, x, y int) {
attachment := math.Point{X: ANIMATION_WIDTH/2 + x, Y: y}
phi := p.GetPhi()
ball := math.Point{X: x + ANIMATION_WIDTH/2 + math.Round(float32(l*omath.Sin(phi))), Y: y + math.Round(float32(l*omath.Cos(phi)))}
line := gxui.Polygon{gxui.PolygonVertex{attachment, 0}, gxui.PolygonVertex{ball, 0}}
canvas.DrawLines(line, gxui.DefaultPen)
m := math.Point{int(BALL_RADIUS), int(BALL_RADIUS)}
rect := math.Rect{ball.Sub(m), ball.Add(m)}
canvas.DrawRoundedRect(rect, BALL_RADIUS, BALL_RADIUS, BALL_RADIUS, BALL_RADIUS, gxui.TransparentPen, gxui.CreateBrush(gxui.Yellow))
}
func appMain(driver gxui.Driver) {
theme := dark.CreateTheme(driver)
window := theme.CreateWindow(ANIMATION_WIDTH, 2*ANIMATION_HEIGHT, "Pendulum")
window.SetBackgroundBrush(gxui.CreateBrush(gxui.Gray50))
image := theme.CreateImage()
ticker := time.NewTicker(time.Millisecond * 15)
pendulum := &mathematicalPendulum{}
pendulum2 := &numericalPendulum{PHI_ZERO, 0.0, 0.0, time.Time{}}
go func() {
for _ = range ticker.C {
canvas := driver.CreateCanvas(math.Size{ANIMATION_WIDTH, 2 * ANIMATION_HEIGHT})
canvas.Clear(gxui.White)
draw(pendulum, canvas, 0, 0)
draw(pendulum2, canvas, 0, ANIMATION_HEIGHT)
canvas.Complete()
driver.Call(func() {
image.SetCanvas(canvas)
})
}
}()
window.AddChild(image)
window.OnClose(ticker.Stop)
window.OnClose(driver.Terminate)
}
func main() {
gl.StartDriver(appMain)
}</syntaxhighlight>
=={{header|Haskell}}==
{{libheader|HGL}}
<syntaxhighlight lang="haskell">import Graphics.HGL.Draw.Monad (Graphic, )
import Graphics.HGL.Draw.Picture
import Graphics.HGL.Utils
import Graphics.HGL.Window
import Graphics.HGL.Run
import Control.Exception (bracket, )
import Control.Arrow
toInt = fromIntegral.round
pendulum = runGraphics $
bracket
(openWindowEx "Pendulum animation task" Nothing (600,400) DoubleBuffered (Just 30))
closeWindow
(\w -> mapM_ ((\ g -> setGraphic w g >> getWindowTick w).
(\ (x, y) -> overGraphic (line (300, 0) (x, y))
(ellipse (x - 12, y + 12) (x + 12, y - 12)) )) pts)
where
dt = 1/30
t = - pi/4
l = 1
g = 9.812
nextAVT (a,v,t) = (a', v', t + v' * dt) where
a' = - (g / l) * sin t
v' = v + a' * dt
pts = map (\(_,t,_) -> (toInt.(300+).(300*).cos &&& toInt. (300*).sin) (pi/2+0.6*t) )
$ iterate nextAVT (- (g / l) * sin t, t, 0)</syntaxhighlight>
Usage with <code>ghci</code>:
*Main> pendulum
=== Alternative solution ===
{{libheader|Gloss}}
<syntaxhighlight lang="haskell">import Graphics.Gloss
-- Initial conditions
g_ = (-9.8) :: Float --Gravity acceleration
v_0 = 0 :: Float --Initial tangential speed
a_0 = 0 / 180 * pi :: Float --Initial angle
dt = 0.01 :: Float --Time step
t_f = 15 :: Float --Final time for data logging
l_ = 200 :: Float --Rod length
-- Define a type to represent the pendulum:
type Pendulum = (Float, Float, Float) -- (rod length, tangential speed, angle)
-- Pendulum's initial state
initialstate :: Pendulum
initialstate = (l_, v_0, a_0)
-- Step funtion: update pendulum to new position
movePendulum :: Float -> Pendulum -> Pendulum
movePendulum dt (l,v,a) = ( l , v_2 , a + v_2 / l * dt*10 )
where v_2 = v + g_ * (cos a) * dt
-- Convert from Pendulum to [Picture] for display
renderPendulum :: Pendulum -> [Picture]
renderPendulum (l,v,a) = map (uncurry Translate newOrigin)
[ Line [ ( 0 , 0 ) , ( l * (cos a), l * (sin a) ) ]
, polygon [ ( 0 , 0 ) , ( -5 , 8.66 ) , ( 5 , 8.66 ) ]
, Translate ( l * (cos a)) (l * (sin a)) (circleSolid (0.04*l_))
, Translate (-1.1*l) (-1.3*l) (Scale 0.1 0.1 (Text currSpeed))
, Translate (-1.1*l) (-1.3*l + 20) (Scale 0.1 0.1 (Text currAngle))
]
where currSpeed = "Speed (pixels/s) = " ++ (show v)
currAngle = "Angle (deg) = " ++ (show ( 90 + a / pi * 180 ) )
-- New origin to beter display the animation
newOrigin = (0, l_ / 2)
-- Calcule a proper window size (for angles between 0 and -pi)
windowSize :: (Int, Int)
windowSize = ( 300 + 2 * round (snd newOrigin)
, 200 + 2 * round (snd newOrigin) )
-- Run simulation
main :: IO ()
main = do --plotOnGNU
simulate window background fps initialstate render update
where window = InWindow "Animate a pendulum" windowSize (40, 40)
background = white
fps = round (1/dt)
render xs = pictures $ renderPendulum xs
update _ = movePendulum</syntaxhighlight>
=={{header|HicEst}}==
[http://www.HicEst.com/DIFFEQ.htm DIFFEQ] and the callback procedure pendulum numerically integrate the pendulum equation.
The display window can be resized during the run, but for window width not equal to 2*height the pendulum rod becomes a rubber band instead:
<syntaxhighlight lang="hicest">REAL :: msec=10, Lrod=1, dBob=0.03, g=9.81, Theta(2), dTheta(2)
BobMargins = ALIAS(ls, rs, ts, bs) ! box margins to draw the bob
Theta = (1, 0) ! initial angle and velocity
start_t = TIME()
DO i = 1, 1E100 ! "forever"
end_t = TIME() ! to integrate in real-time sections:
DIFFEQ(Callback="pendulum", T=end_t, Y=Theta, DY=dTheta, T0=start_t)
xBob = (SIN(Theta(1)) + 1) / 2
yBob = COS(Theta(1)) - dBob
! create or clear window and draw pendulum bob at (xBob, yBob):
WINDOW(WIN=wh, LeftSpace=0, RightSpace=0, TopSpace=0, BottomSpace=0, Up=999)
BobMargins = (xBob-dBob, 1-xBob-dBob, yBob-dBob, 1-yBob-dBob)
WINDOW(WIN=wh, LeftSpace=ls, RightSpace=rs, TopSpace=ts, BottomSpace=bs)
WRITE(WIN=wh, DeCoRation='EL=4, BC=4') ! flooded red ellipse as bob
! draw the rod hanging from the center of the window:
WINDOW(WIN=wh, LeftSpace=0.5, TopSpace=0, RightSpace=rs+dBob)
WRITE(WIN=wh, DeCoRation='LI=0 0; 1 1, FC=4.02') ! red pendulum rod
SYSTEM(WAIT=msec)
start_t = end_t
ENDDO
END
SUBROUTINE pendulum ! Theta" = - (g/Lrod) * SIN(Theta)
dTheta(1) = Theta(2) ! Theta' = Theta(2) substitution
dTheta(2) = -g/Lrod*SIN(Theta(1)) ! Theta" = Theta(2)' = -g/Lrod*SIN(Theta(1))
END</syntaxhighlight>
== Icon and {{header|Unicon}} ==
The following code uses features exclusive to Unicon, specifically the object-oriented gui library.
{{trans|Scheme}}
<syntaxhighlight lang="unicon">
import gui
$include "guih.icn"
# some constants to define the display and pendulum
$define HEIGHT 400
$define WIDTH 500
$define STRING_LENGTH 200
$define HOME_X 250
$define HOME_Y 21
$define SIZE 30
$define START_ANGLE 80
class WindowApp : Dialog ()
# draw the pendulum on given context_window, at position (x,y)
method draw_pendulum (x, y)
# reference to current screen area to draw on
cw := Clone(self.cwin)
# clear screen
WAttrib (cw, "bg=grey")
EraseRectangle (cw, 0, 0, WIDTH, HEIGHT)
# draw the display
WAttrib (cw, "fg=dark gray")
DrawLine (cw, 10, 20, WIDTH-20, 20)
WAttrib (cw, "fg=black")
DrawLine (cw, HOME_X, HOME_Y, x, y)
FillCircle (cw, x, y, SIZE+2)
WAttrib (cw, "fg=yellow")
FillCircle (cw, x, y, SIZE)
# free reference to screen area
Uncouple (cw)
end
# find the average of given two arguments
method avg (a, b)
return (a + b) / 2
end
# this method gets called by the ticker
# it computes the next position of the pendulum and
# requests a redraw
method tick ()
static x, y
static theta := START_ANGLE
static d_theta := 0
# update x,y of pendulum
scaling := 3000.0 / (STRING_LENGTH * STRING_LENGTH)
# -- first estimate
first_dd_theta := -(sin (dtor (theta)) * scaling)
mid_d_theta := d_theta + first_dd_theta
mid_theta := theta + avg (d_theta, mid_d_theta)
# -- second estimate
mid_dd_theta := - (sin (dtor (mid_theta)) * scaling)
mid_d_theta_2 := d_theta + avg (first_dd_theta, mid_dd_theta)
mid_theta_2 := theta + avg (d_theta, mid_d_theta_2)
# -- again first
mid_dd_theta_2 := -(sin (dtor (mid_theta_2)) * scaling)
last_d_theta := mid_d_theta_2 + mid_dd_theta_2
last_theta := mid_theta_2 + avg (mid_d_theta_2, last_d_theta)
# -- again second
last_dd_theta := - (sin (dtor (last_theta)) * scaling)
last_d_theta_2 := mid_d_theta_2 + avg (mid_dd_theta_2, last_dd_theta)
last_theta_2 := mid_theta_2 + avg (mid_d_theta_2, last_d_theta_2)
# -- update stored angles
d_theta := last_d_theta_2
theta := last_theta_2
# -- update x, y
pendulum_angle := dtor (theta)
x := HOME_X + STRING_LENGTH * sin (pendulum_angle)
y := HOME_Y + STRING_LENGTH * cos (pendulum_angle)
# draw pendulum
draw_pendulum (x, y)
end
# set up the window
method component_setup ()
# some cosmetic settings for the window
attrib("size="||WIDTH||","||HEIGHT, "bg=light gray", "label=Pendulum")
# make sure we respond to window close event
connect (self, "dispose", CLOSE_BUTTON_EVENT)
# start the ticker, to update the display periodically
self.set_ticker (20)
end
end
procedure main ()
w := WindowApp ()
w.show_modal ()
end
</syntaxhighlight>
=={{header|J}}==
Works for '''J6'''
<syntaxhighlight lang="j">require 'gl2 trig'
coinsert 'jgl2'
DT =: %30 NB. seconds
ANGLE=: 0.45p1 NB. radians
L =: 1 NB. metres
G =: 9.80665 NB. ms_2
VEL =: 0 NB. ms_1
PEND=: noun define
pc pend;pn "Pendulum";
xywh 0 0 320 200;cc isi isigraph rightmove bottommove;
pas 0 0;pcenter;
rem form end;
)
pend_run =: verb def ' wd PEND,'';pshow;timer '',":DT * 1000 '
pend_close =: verb def ' wd ''timer 0; pclose'' '
pend_isi_paint=: verb def ' drawPendulum ANGLE '
sys_timer_z_=: verb define
recalcAngle ''
wd 'psel pend; setinvalid isi'
)
recalcAngle=: verb define
accel=. - (G % L) * sin ANGLE
VEL =: VEL + accel * DT
ANGLE=: ANGLE + VEL * DT
)
drawPendulum=: verb define
width=. {. glqwh''
ps=. (-: width) , 40
pe=. ps + 280 <.@* (cos , sin) 0.5p1 + y NB. adjust orientation
glbrush glrgb 91 91 91
gllines ps , pe
glellipse (,~ ps - -:) 40 15
glellipse (,~ pe - -:) 20 20
glrect 0 0 ,width, 40
)
pend_run'' NB. run animation</syntaxhighlight>
Updated for changes in '''J8'''
<syntaxhighlight lang="j">require 'gl2 trig'
coinsert 'jgl2'
DT =: %30 NB. seconds
ANGLE=: 0.45p1 NB. radians
L =: 1 NB. metres
G =: 9.80665 NB. ms_2
VEL =: 0 NB. ms_1
PEND=: noun define
pc pend;pn "Pendulum";
minwh 320 200; cc isi isigraph flush;
)
pend_run=: verb define
wd PEND,'pshow'
wd 'timer ',":DT * 1000
)
pend_close=: verb define
wd 'timer 0; pclose'
)
sys_timer_z_=: verb define
recalcAngle_base_ ''
wd 'psel pend; set isi invalid'
)
pend_isi_paint=: verb define
drawPendulum ANGLE
)
recalcAngle=: verb define
accel=. - (G % L) * sin ANGLE
VEL =: VEL + accel * DT
ANGLE=: ANGLE + VEL * DT
)
drawPendulum=: verb define
width=. {. glqwh''
ps=. (-: width) , 20
pe=. ps + 150 <.@* (cos , sin) 0.5p1 + y NB. adjust orientation
glclear''
glbrush glrgb 91 91 91 NB. gray
gllines ps , pe
glellipse (,~ ps - -:) 40 15
glrect 0 0, width, 20
glbrush glrgb 255 255 0 NB. yellow
glellipse (,~ pe - -:) 15 15 NB. orb
)
pend_run''</syntaxhighlight>
[[File:J_pendulum.gif|320px|pretend the ball is yellow - gifgrabber grabbed a monochrome image for some reason...]]
=={{header|Java}}==
{{libheader|Swing}} {{libheader|AWT}}
<syntaxhighlight lang="java">import java.awt.*;
import javax.swing.*;
public class Pendulum extends JPanel implements Runnable {
private double angle = Math.PI / 2;
private int length;
public Pendulum(int length) {
this.length = length;
setDoubleBuffered(true);
}
@Override
public void paint(Graphics g) {
g.setColor(Color.WHITE);
g.fillRect(0, 0, getWidth(), getHeight());
g.setColor(Color.BLACK);
int anchorX = getWidth() / 2, anchorY = getHeight() / 4;
int ballX = anchorX + (int) (Math.sin(angle) * length);
int ballY = anchorY + (int) (Math.cos(angle) * length);
g.drawLine(anchorX, anchorY, ballX, ballY);
g.fillOval(anchorX - 3, anchorY - 4, 7, 7);
g.fillOval(ballX - 7, ballY - 7, 14, 14);
}
public void run() {
double angleAccel, angleVelocity = 0, dt = 0.1;
while (true) {
angleAccel = -9.81 / length * Math.sin(angle);
angleVelocity += angleAccel * dt;
angle += angleVelocity * dt;
repaint();
try { Thread.sleep(15); } catch (InterruptedException ex) {}
}
}
@Override
public Dimension getPreferredSize() {
return new Dimension(2 * length + 50, length / 2 * 3);
}
public static void main(String[] args) {
JFrame f = new JFrame("Pendulum");
Pendulum p = new Pendulum(200);
f.add(p);
f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
f.pack();
f.setVisible(true);
new Thread(p).start();
}
}</syntaxhighlight>
=={{header|JavaScript}}==
===With <canvas>===
{{trans|E}} (plus gratuitous motion blur)
<syntaxhighlight lang="javascript"><html><head>
<title>Pendulum</title>
</head><body style="background: gray;">
<canvas id="canvas" width="600" height="600">
<p>Sorry, your browser does not support the <canvas> used to display the pendulum animation.</p>
</canvas>
<script>
function PendulumSim(length_m, gravity_mps2, initialAngle_rad, timestep_ms, callback) {
var velocity = 0;
var angle = initialAngle_rad;
var k = -gravity_mps2/length_m;
var timestep_s = timestep_ms / 1000;
return setInterval(function () {
var acceleration = k * Math.sin(angle);
velocity += acceleration * timestep_s;
angle += velocity * timestep_s;
callback(angle);
}, timestep_ms);
}
var canvas = document.getElementById('canvas');
var context = canvas.getContext('2d');
var prev=0;
var sim = PendulumSim(1, 9.80665, Math.PI*99/100, 10, function (angle) {
var rPend = Math.min(canvas.width, canvas.height) * 0.47;
var rBall = Math.min(canvas.width, canvas.height) * 0.02;
var rBar = Math.min(canvas.width, canvas.height) * 0.005;
var ballX = Math.sin(angle) * rPend;
var ballY = Math.cos(angle) * rPend;
context.fillStyle = "rgba(255,255,255,0.51)";
context.globalCompositeOperation = "destination-out";
context.fillRect(0, 0, canvas.width, canvas.height);
context.fillStyle = "yellow";
context.strokeStyle = "rgba(0,0,0,"+Math.max(0,1-Math.abs(prev-angle)*10)+")";
context.globalCompositeOperation = "source-over";
context.save();
context.translate(canvas.width/2, canvas.height/2);
context.rotate(angle);
context.beginPath();
context.rect(-rBar, -rBar, rBar*2, rPend+rBar*2);
context.fill();
context.stroke();
context.beginPath();
context.arc(0, rPend, rBall, 0, Math.PI*2, false);
context.fill();
context.stroke();
context.restore();
prev=angle;
});
</script>
</body></html></syntaxhighlight>
===Within SVG===
If we use SVG we don't even have to make a HTML document. We can put the script inside SVG.
To do things a bit differently, we'll use a [[wp:stereographic projection|stereographic projection]] of the circle, in order to get algebraic [[wp:Euler-Lagrange equations|Euler-Lagrange equations]] which we'll integrate with the [[Runge-Kutta method]].
Also we'll use a dimensionless formulation of the problem (taking unit value for the mass, the length and so on).
<syntaxhighlight lang="javascript"><svg height="100%" width="100%" viewBox="-2 0 4 4" xmlns="http://www.w3.org/2000/svg">
<line id="string" x1="0" y1="0" x2="1" y2="0" stroke="grey" stroke-width="0.05" />
<circle id="ball" cx="0" cy="0" r="0.1" fill="black" />
<script>
/*jshint esnext: true */
function rk4(dt, x, f) {
"use strict";
let from = Array.from,
a = from(f(from(x, $ => $ )), $ => $*dt),
b = from(f(from(x, ($,i) => $ + a[i]/2)), $ => $*dt),
c = from(f(from(x, ($,i) => $ + b[i]/2)), $ => $*dt),
d = from(f(from(x, ($,i) => $ + c[i] )), $ => $*dt);
return from(x, (_,i) => (a[i] + 2*b[i] + 2*c[i] + d[i])/6);
}
function setPendulumPos($) {
const string = document.getElementById("string"),
ball = document.getElementById("ball");
let $2 = $*$,
x = 2*$/(1+$2),
y = (1-$2)/(1+$2);
string.setAttribute("x2", x);
string.setAttribute("y2", y);
ball.setAttribute("cx", x);
ball.setAttribute("cy", y);
}
var q = [1, 0];
var previousTimestamp;
(function animate(timestamp) {
if ( previousTimestamp !== undefined) {
let dq = rk4((timestamp - previousTimestamp)/1000, q, $ => [$[1], 2*$[1]*$[1]*$[0]/(1+$[0]*$[0]) - $[0]]);
q = [q[0] + dq[0], q[1] + dq[1]];
setPendulumPos(q[0]);
}
previousTimestamp = timestamp;
window.requestAnimationFrame(animate);
})()
</script>
</svg>
</syntaxhighlight>
=={{header|Julia}}==
Differential equation based solution using the Luxor graphics library.<syntaxhighlight lang="julia">using Luxor
using Colors
using BoundaryValueDiffEq
# constants for differential equations and movie
const g = 9.81
const L = 1.0 # pendulum length in meters
const bobd = 0.10 # pendulum bob diameter in meters
const framerate = 50.0 # intended frame rate/sec
const t0 = 0.0 # start time (s)
const tf = 2.3 # end simulation time (s)
const dtframe = 1.0/framerate # time increment per frame
const tspan = LinRange(t0, tf, Int(floor(tf*framerate))) # array of time points in animation
const bgcolor = "black" # gif background
const leaderhue = (0.80, 0.70, 0.20) # gif swing arm hue light gold
const hslcolors = [HSL(col) for col in (distinguishable_colors(
Int(floor(tf*framerate)+3),[RGB(1,1,1)])[2:end])]
const giffilename = "pendulum.gif" # output file
# differential equations
simplependulum(du, u, p, t) = (θ=u[1]; dθ=u[2]; du[1]=dθ; du[2]=-(g/L)*sin(θ))
bc2(residual, u, p, t) = (residual[1] = u[end÷2][1] + pi/2; residual[2] = u[end][1] - pi/2)
bvp2 = BVProblem(simplependulum, bc2, [pi/2,pi/2], (tspan[1],tspan[end]))
sol2 = solve(bvp2, MIRK4(), dt=dtframe) # use the MIRK4 solver for TwoPointBVProblem
# movie making background
backdrop(scene, framenumber) = background(bgcolor)
function frame(scene, framenumber)
u1, u2 = sol2.u[framenumber]
y, x = L*cos(u1), L*sin(u1)
sethue(leaderhue)
poly([Point(-4.0, 0.0), Point(4.0, 0.0),
Point(160.0x,160.0y)], :fill)
sethue(Colors.HSV(framenumber*4.0, 1, 1))
circle(Point(160.0x,160.0y), 160bobd, :fill)
text(string("frame $framenumber of $(scene.framerange.stop)"),
Point(0.0, -190.0),
halign=:center)
end
muv = Movie(400, 400, "Pendulum Demo", 1:length(tspan))
animate(muv, [Scene(muv, backdrop),
Scene(muv, frame, easingfunction=easeinoutcubic)],
creategif=true, pathname=giffilename)</syntaxhighlight>
{{out}}
[[File:Pendulum animation.gif|320px]]
<pre>
</pre>
=={{header|Kotlin}}==
Conversion of Java snippet.
<syntaxhighlight lang="scala">import java.awt.*
import java.util.concurrent.*
import javax.swing.*
class Pendulum(private val length: Int) : JPanel(), Runnable {
init {
val f = JFrame("Pendulum")
f.add(this)
f.defaultCloseOperation = JFrame.EXIT_ON_CLOSE
f.pack()
f.isVisible = true
isDoubleBuffered = true
}
override fun paint(g: Graphics) {
with(g) {
color = Color.WHITE
fillRect(0, 0, width, height)
color = Color.BLACK
val anchor = Element(width / 2, height / 4)
val ball = Element((anchor.x + Math.sin(angle) * length).toInt(), (anchor.y + Math.cos(angle) * length).toInt())
drawLine(anchor.x, anchor.y, ball.x, ball.y)
fillOval(anchor.x - 3, anchor.y - 4, 7, 7)
fillOval(ball.x - 7, ball.y - 7, 14, 14)
}
}
override fun run() {
angleVelocity += -9.81 / length * Math.sin(angle) * dt
angle += angleVelocity * dt
repaint()
}
override fun getPreferredSize() = Dimension(2 * length + 50, length / 2 * 3)
private data class Element(val x: Int, val y: Int)
private val dt = 0.1
private var angle = Math.PI / 2
private var angleVelocity = 0.0
}
fun main(a: Array<String>) {
val executor = Executors.newSingleThreadScheduledExecutor()
executor.scheduleAtFixedRate(Pendulum(200), 0, 15, TimeUnit.MILLISECONDS)
}</syntaxhighlight>
=={{header|Liberty BASIC}}==
<syntaxhighlight lang="lb">nomainwin
WindowWidth = 400
WindowHeight = 300
open "Pendulum" for graphics_nsb_nf as #main
#main "down;fill white; flush"
#main "color black"
#main "trapclose [quit.main]"
Angle = asn(1)
DeltaT = 0.1
PendLength = 150
FixX = int(WindowWidth / 2)
FixY = 40
timer 30, [swing]
wait
[swing]
#main "cls"
#main "discard"
PlumbobX = FixX + int(sin(Angle) * PendLength)
PlumbobY = FixY + int(cos(Angle) * PendLength)
AngAccel = -9.81 / PendLength * sin(Angle)
AngVelocity = AngVelocity + AngAccel * DeltaT
Angle = Angle + AngVelocity * DeltaT
#main "backcolor black"
#main "place ";FixX;" ";FixY
#main "circlefilled 3"
#main "line ";FixX;" ";FixY;" ";PlumbobX;" ";PlumbobY
#main "backcolor red"
#main "circlefilled 10"
wait
[quit.main]
close #main
end</syntaxhighlight>
=={{header|Lingo}}==
<syntaxhighlight lang="lingo">global RODLEN, GRAVITY, DT
global velocity, acceleration, angle, posX, posY
on startMovie
-- window properties
_movie.stage.title = "Pendulum"
_movie.stage.titlebarOptions.visible = TRUE
_movie.stage.rect = rect(0, 0, 400, 400)
_movie.centerStage = TRUE
_movie.puppetTempo(30)
RODLEN = 180
GRAVITY = -9.8
DT = 0.03
velocity = 0.0
acceleration = 0.0
angle = PI/3
posX = 200 - sin(angle) * RODLEN
posY = 100 + cos(angle) * RODLEN
paint()
-- show the window
_movie.stage.visible = TRUE
end
on enterFrame
acceleration = GRAVITY * sin(angle)
velocity = velocity + acceleration * DT
angle = angle + velocity * DT
posX = 200 - sin(angle) * rodLen
posY = 100 + cos(angle) * rodLen
paint()
end
on paint
img = _movie.stage.image
img.fill(img.rect, rgb(255,255,255))
img.fill(point(200-5, 100-5), point(200+5, 100+5), [#shapeType:#oval,#color:rgb(0,0,0)])
img.draw(point(200, 100), point(posX, posY), [#color:rgb(0,0,0)])
img.fill(point(posX-20, posY-20), point(posX+20, posY+20), [#shapeType:#oval,#lineSize:1,#bgColor:rgb(0,0,0),#color:rgb(255,255,0)])
end</syntaxhighlight>
=={{header|Logo}}==
{{works with|UCB Logo}}
<syntaxhighlight lang="logo">make "angle 45
make "L 1
make "bob 10
Line 273 ⟶ 2,879:
hideturtle
until [key?] [step.pendulum]</syntaxhighlight>
=={{header|
Needs LÖVE 2D Engine
<syntaxhighlight lang="lua">
function degToRad( d )
return d * 0.01745329251
end
function love.load()
g = love.graphics
rodLen, gravity, velocity, acceleration = 260, 3, 0, 0
halfWid, damp = g.getWidth() / 2, .989
posX, posY, angle = halfWid
TWO_PI, angle = math.pi * 2, degToRad( 90 )
end
function love.update( dt )
acceleration = -gravity / rodLen * math.sin( angle )
angle = angle + velocity; if angle > TWO_PI then angle = 0 end
velocity = velocity + acceleration
velocity = velocity * damp
posX = halfWid + math.sin( angle ) * rodLen
posY = math.cos( angle ) * rodLen
end
function love.draw()
g.setColor( 250, 0, 250 )
g.circle( "fill", halfWid, 0, 8 )
g.line( halfWid, 4, posX, posY )
g.setColor( 250, 100, 20 )
g.circle( "fill", posX, posY, 20 )
end
</syntaxhighlight>
=={{header|M2000 Interpreter}}==
<syntaxhighlight lang="m2000 interpreter">
Module Pendulum {
back()
degree=180/pi
THETA=Pi/2
SPEED=0
G=9.81
L=0.5
Profiler
lasttimecount=0
cc=40 ' 40 ms every draw
accold=0
Every cc {
ACCEL=G*SIN(THETA*degree)/L/50
SPEED+=ACCEL/cc
THETA+=SPEED
Pendulum(THETA)
if KeyPress(32) Then Exit
}
Sub back()
If not IsWine then Smooth On
Cls 7,0
Pen 0
Move 0, scale.y/4
Draw scale.x,0
Step -scale.x/2
circle fill #AAAAAA, scale.x/50
Hold ' hold this as background
End Sub
Sub Pendulum(x)
x+=pi/2
Release ' place stored background to screen
Width scale.x/2000 {
Draw Angle x, scale.y/2.5
Width 1 {
Circle Fill 14, scale.x/25
}
Step Angle x, -scale.y/2.5
}
Print @(1,1), lasttimecount
if sgn(accold)<>sgn(ACCEL) then lasttimecount=timecount: Profiler
accold=ACCEL
Refresh 1000
End Sub
}
Pendulum
</syntaxhighlight>
=={{header|Mathematica}} / {{header|Wolfram Language}}==
<syntaxhighlight lang="mathematica">tmax = 10;
g = 9.8;
l = 1;
pendulum = Module[
{g, l},
ParametricNDSolve[
{
y''[t] + g/l Sin[y[t]] == 0,
y[0] == 0, y'[0] == 1
},
{y},
{t, 0, tmax},
{g, l}
]
];
Animate[
Graphics[
Rotate[
{Line[{{0, 0}, {0, -1}}], Disk[{0, -1}, .1]},
Evaluate[y[g, l] /. pendulum][t],
{0, 0}
],
PlotRange -> {{-l, l}, {-l - .5, 0}}
],
{t, 0, tmax},
AnimationRate -> 1
]</syntaxhighlight>
=={{header|MATLAB}}==
pendulum.m
<syntaxhighlight lang="matlab">%This is a numerical simulation of a pendulum with a massless pivot arm.
%% User Defined Parameters
%Define external parameters
g = -9.8;
deltaTime = 1/50; %Decreasing this will increase simulation accuracy
endTime = 16;
%Define pendulum
rodPivotPoint = [2 2]; %rectangular coordinates
rodLength = 1;
mass = 1; %of the bob
radius = .2; %of the bob
theta = 45; %degrees, defines initial position of the bob
velocity = [0 0]; %cylindrical coordinates; first entry is radial velocity,
%second entry is angular velocity
%% Simulation
assert(radius < rodLength,'Pendulum bob radius must be less than the length of the rod.');
position = rodPivotPoint - (rodLength*[-sind(theta) cosd(theta)]); %in rectangular coordinates
%Generate graphics, render pendulum
figure;
axesHandle = gca;
xlim(axesHandle, [(rodPivotPoint(1) - rodLength - radius) (rodPivotPoint(1) + rodLength + radius)] );
ylim(axesHandle, [(rodPivotPoint(2) - rodLength - radius) (rodPivotPoint(2) + rodLength + radius)] );
rectHandle = rectangle('Position',[(position - radius/2) radius radius],...
'Curvature',[1,1],'FaceColor','g'); %Pendulum bob
hold on
plot(rodPivotPoint(1),rodPivotPoint(2),'^'); %pendulum pivot
lineHandle = line([rodPivotPoint(1) position(1)],...
[rodPivotPoint(2) position(2)]); %pendulum rod
hold off
%Run simulation, all calculations are performed in cylindrical coordinates
for time = (deltaTime:deltaTime:endTime)
drawnow; %Forces MATLAB to render the pendulum
%Find total force
gravitationalForceCylindrical = [mass*g*cosd(theta) mass*g*sind(theta)];
%This code is just incase you want to add more forces,e.g friction
totalForce = gravitationalForceCylindrical;
%If the rod isn't massless or is a spring, etc., modify this line
%accordingly
rodForce = [-totalForce(1) 0]; %cylindrical coordinates
totalForce = totalForce + rodForce;
acceleration = totalForce / mass; %F = ma
velocity = velocity + acceleration * deltaTime;
rodLength = rodLength + velocity(1) * deltaTime;
theta = theta + velocity(2) * deltaTime; % Attention!! Mistake here.
% Velocity needs to be divided by pendulum length and scaled to degrees:
% theta = theta + velocity(2) * deltaTime/rodLength/pi*180;
position = rodPivotPoint - (rodLength*[-sind(theta) cosd(theta)]);
%Update figure with new position info
set(rectHandle,'Position',[(position - radius/2) radius radius]);
set(lineHandle,'XData',[rodPivotPoint(1) position(1)],'YData',...
[rodPivotPoint(2) position(2)]);
end</syntaxhighlight>
=={{header|Nim}}==
===OpenGL version===
{{trans|C}}
{{libheader|OpenGL}}
{{libheader|Nim bindings for OpenGL}}
Conversion from C with some modifications: changing some variable names, adding a display function to make the program work with "freeGlut", choosing another initial angle, etc.
<syntaxhighlight lang="nim"># Pendulum simulation.
import math
import times
import opengl
import opengl/glut
var
# Simulation variables.
lg: float # Pendulum length.
g: float # Gravity (should be positive).
currTime: Time # Current time.
theta0: float # Initial angle.
theta: float # Current angle.
omega: float # Angular velocity = derivative of theta.
accel: float # Angular acceleration = derivative of omega.
e: float # Total energy.
#---------------------------------------------------------------------------------------------------
proc initSimulation(length, gravitation, start: float) =
## Initialize the simulation.
lg = length
g = gravitation
currTime = getTime()
theta0 = start # Initial angle for which omega = 0.
theta = start
omega = 0
accel = -g / lg * sin(theta0)
e = g * lg * (1 - cos(theta0)) # Total energy = potential energy when starting.
#---------------------------------------------------------------------------------------------------
proc elapsed(): float =
## Return the elapsed time since previous call, expressed in seconds.
let nextTime = getTime()
result = (nextTime - currTime).inMicroseconds.float / 1e6
currTime = nextTime
#---------------------------------------------------------------------------------------------------
proc resize(w, h: GLsizei) =
## Resize the window.
glViewport(0, 0, w, h)
glMatrixMode(GL_PROJECTION)
glLoadIdentity()
glMatrixMode(GL_MODELVIEW)
glLoadIdentity()
glOrtho(0, GLdouble(w), GLdouble(h), 0, -1, 1)
#---------------------------------------------------------------------------------------------------
proc render() {.cdecl.} =
## Render the window.
# Compute the position of the mass.
var x = 320 + 300 * sin(theta)
var y = 300 * cos(theta)
resize(640, 320)
glClear(GL_COLOR_BUFFER_BIT)
# Draw the line from pivot to mass.
glBegin(GL_LINES)
glVertex2d(320, 0)
glVertex2d(x, y)
glEnd()
glFlush()
# Update theta and omega.
let dt = elapsed()
theta += (omega + dt * accel / 2) * dt
omega += accel * dt
# If, due to computation errors, potential energy is greater than total energy,
# reset theta to ±theta0 and omega to 0.
if lg * g * (1 - cos(theta)) >= e:
theta = sgn(theta).toFloat * theta0
omega = 0
accel = -g / lg * sin(theta)
#---------------------------------------------------------------------------------------------------
proc initGfx(argc: ptr cint; argv: pointer) =
## Initialize OpenGL rendering.
glutInit(argc, argv)
glutInitDisplayMode(GLUT_RGB)
glutInitWindowSize(640, 320)
glutIdleFunc(render)
discard glutCreateWindow("Pendulum")
glutDisplayFunc(render)
loadExtensions()
#———————————————————————————————————————————————————————————————————————————————————————————————————
initSimulation(length = 5, gravitation = 9.81, start = PI / 3)
var argc: cint = 0
initGfx(addr(argc), nil)
glutMainLoop()</syntaxhighlight>
===Gtk3 version===
{{libheader|gintro}}
This version uses the same equations but replace OpenGL by Gtk3 with the “gintro” bindings.
<syntaxhighlight lang="nim"># Pendulum simulation.
import math
import times
import gintro/[gobject, gdk, gtk, gio, cairo]
import gintro/glib except Pi
type
# Description of the simulation.
Simulation = ref object
area: DrawingArea # Drawing area.
length: float # Pendulum length.
g: float # Gravity (should be positive).
time: Time # Current time.
theta0: float # initial angle.
theta: float # Current angle.
omega: float # Angular velocity = derivative of theta.
accel: float # Angular acceleration = derivative of omega.
e: float # Total energy.
#---------------------------------------------------------------------------------------------------
proc newSimulation(area: DrawingArea; length, g, theta0: float): Simulation {.noInit.} =
## Allocate and initialize the simulation object.
new(result)
result.area = area
result.length = length
result.g = g
result.time = getTime()
result.theta0 = theta0
result.theta = theta0
result.omega = 0
result.accel = -g / length * sin(theta0)
result.e = g * length * (1 - cos(theta0)) # Total energy = potential energy when starting.
#---------------------------------------------------------------------------------------------------
template toFloat(dt: Duration): float = dt.inNanoseconds.float / 1e9
#---------------------------------------------------------------------------------------------------
const Origin = (x: 320.0, y: 100.0) # Pivot coordinates.
const Scale = 300 # Coordinates scaling constant.
proc draw(sim: Simulation; context: cairo.Context) =
## Draw the pendulum.
# Compute coordinates in drawing area.
let x = Origin.x + sin(sim.theta) * Scale
let y = Origin.y + cos(sim.theta) * Scale
# Clear the region.
context.moveTo(0, 0)
context.setSource(0.0, 0.0, 0.0)
context.paint()
# Draw pendulum.
context.moveTo(Origin.x, Origin.y)
context.setSource(0.3, 1.0, 0.3)
context.lineTo(x, y)
context.stroke()
# Draw pivot.
context.setSource(0.3, 0.3, 1.0)
context.arc(Origin.x, Origin.y, 8, 0, 2 * Pi)
context.fill()
# Draw mass.
context.setSource(1.0, 0.3, 0.3)
context.arc(x, y, 8, 0, 2 * Pi)
context.fill()
#---------------------------------------------------------------------------------------------------
proc update(sim: Simulation): gboolean =
## Update the simulation state.
# compute time interval.
let nextTime = getTime()
let dt = (nextTime - sim.time).toFloat
sim.time = nextTime
# Update theta and omega.
sim.theta += (sim.omega + dt * sim.accel / 2) * dt
sim.omega += sim.accel * dt
# If, due to computation errors, potential energy is greater than total energy,
# reset theta to ±theta0 and omega to 0.
if sim.length * sim.g * (1 - cos(sim.theta)) >= sim.e:
sim.theta = sgn(sim.theta).toFloat * sim.theta0
sim.omega = 0
# Compute acceleration.
sim.accel = -sim.g / sim.length * sin(sim.theta)
result = gboolean(1)
sim.draw(sim.area.window.cairoCreate())
#---------------------------------------------------------------------------------------------------
proc activate(app: Application) =
## Activate the application.
let window = app.newApplicationWindow()
window.setSizeRequest(640, 480)
window.setTitle("Pendulum simulation")
let area = newDrawingArea()
window.add(area)
let sim = newSimulation(area, length = 5, g = 9.81, theta0 = PI / 3)
timeoutAdd(10, update, sim)
window.showAll()
#———————————————————————————————————————————————————————————————————————————————————————————————————
let app = newApplication(Application, "Rosetta.pendulum")
discard app.connect("activate", activate)
discard app.run()</syntaxhighlight>
=={{header|ooRexx}}==
ooRexx does not have a portable GUI, but this version is similar to the Ada version and just prints out the coordinates of the end of the pendulum.
<syntaxhighlight lang="oorexx">
pendulum = .pendulum~new(10, 30)
before = .datetime~new
do 100 -- somewhat arbitrary loop count
call syssleep .2
now = .datetime~new
pendulum~update(now - before)
before = now
say " X:" pendulum~x " Y:" pendulum~y
end
::class pendulum
::method init
expose length theta x y velocity
use arg length, theta
x = rxcalcsin(theta) * length
y = rxcalccos(theta) * length
velocity = 0
::attribute x GET
::attribute y GET
::constant g -9.81 -- acceleration due to gravity
::method update
expose length theta x y velocity
use arg duration
acceleration = self~g / length * rxcalcsin(theta)
durationSeconds = duration~microseconds / 1000000
x = rxcalcsin(theta, length)
y = rxcalccos(theta, length)
velocity = velocity + acceleration * durationSeconds
theta = theta + velocity * durationSeconds
::requires rxmath library
</syntaxhighlight>
=={{header|Oz}}==
Inspired by the E and Ruby versions.
<syntaxhighlight lang="oz">declare
[QTk] = {Link ['x-oz://system/wp/QTk.ozf']}
Pi = 3.14159265
class PendulumModel
feat
K
attr
angle
velocity
meth init(length:L <= 1.0 %% meters
gravity:G <= 9.81 %% m/s²
initialAngle:A <= Pi/2.) %% radians
self.K = ~G / L
angle := A
velocity := 0.0
end
meth nextAngle(deltaT:DeltaTMS %% milliseconds
?Angle) %% radians
DeltaT = {Int.toFloat DeltaTMS} / 1000.0 %% seconds
Acceleration = self.K * {Sin @angle}
in
velocity := @velocity + Acceleration * DeltaT
angle := @angle + @velocity * DeltaT
Angle = @angle
end
end
%% Animates a pendulum on a given canvas.
class PendulumAnimation from Time.repeat
feat
Pend
Rod
Bob
home:pos(x:160 y:50)
length:140.0
delay
meth init(Pendulum Canvas delay:Delay <= 25) %% milliseconds
self.Pend = Pendulum
self.delay = Delay
%% plate and pivot
{Canvas create(line 0 self.home.y 320 self.home.y width:2 fill:grey50)}
{Canvas create(oval 155 self.home.y-5 165 self.home.y+5 fill:grey50 outline:black)}
%% the pendulum itself
self.Rod = {Canvas create(line 1 1 1 1 width:3 fill:black handle:$)}
self.Bob = {Canvas create(oval 1 1 2 2 fill:yellow outline:black handle:$)}
%%
{self setRepAll(action:Animate delay:Delay)}
end
meth Animate
Theta = {self.Pend nextAngle(deltaT:self.delay $)}
%% calculate x and y from angle
X = self.home.x + {Float.toInt self.length * {Sin Theta}}
Y = self.home.y + {Float.toInt self.length * {Cos Theta}}
in
%% update canvas
try
{self.Rod setCoords(self.home.x self.home.y X Y)}
{self.Bob setCoords(X-15 Y-15 X+15 Y+15)}
catch system(tk(alreadyClosed ...) ...) then skip end
end
end
Pendulum = {New PendulumModel init}
Canvas
GUI = td(title:"Pendulum"
canvas(width:320 height:210 handle:?Canvas)
action:proc {$} {Animation stop} {Window close} end
)
Window = {QTk.build GUI}
Animation = {New PendulumAnimation init(Pendulum Canvas)}
in
{Window show}
{Animation go}
</syntaxhighlight>
=={{header|Perl}}==
{{libheader|Perl/Tk}}
{{trans|Tcl}}
This does not have the window resizing handling that Tcl does
<syntaxhighlight lang="perl">
use strict;
use warnings;
use Tk;
use Math::Trig qw/:pi/;
my $root = new MainWindow( -title => 'Pendulum Animation' );
my $canvas = $root->Canvas(-width => 320, -height => 200);
my $after_id;
for ($canvas) {
$_->createLine( 0, 25, 320, 25, -tags => [qw/plate/], -width => 2, -fill => 'grey50' );
$_->createOval( 155, 20, 165, 30, -tags => [qw/pivot outline/], -fill => 'grey50' );
$_->createLine( 1, 1, 1, 1, -tags => [qw/rod width/], -width => 3, -fill => 'black' );
$_->createOval( 1, 1, 2, 2, -tags => [qw/bob outline/], -fill => 'yellow' );
}
$canvas->raise('pivot');
$canvas->pack(-fill => 'both', -expand => 1);
my ($Theta, $dTheta, $length, $homeX, $homeY) =
(45, 0, 150, 160, 25);
sub show_pendulum {
my $angle = $Theta * pi() / 180;
my $x = $homeX + $length * sin($angle);
my $y = $homeY + $length * cos($angle);
$canvas->coords('rod', $homeX, $homeY, $x, $y);
$canvas->coords('bob', $x-15, $y-15, $x+15, $y+15);
}
sub recompute_angle {
my $scaling = 3000.0 / ($length ** 2);
# first estimate
my $firstDDTheta = -sin($Theta * pi / 180) * $scaling;
my $midDTheta = $dTheta + $firstDDTheta;
my $midTheta = $Theta + ($dTheta + $midDTheta)/2;
# second estimate
my $midDDTheta = -sin($midTheta * pi/ 180) * $scaling;
$midDTheta = $dTheta + ($firstDDTheta + $midDDTheta)/2;
$midTheta = $Theta + ($dTheta + $midDTheta)/2;
# again, first
$midDDTheta = -sin($midTheta * pi/ 180) * $scaling;
my $lastDTheta = $midDTheta + $midDDTheta;
my $lastTheta = $midTheta + ($midDTheta + $lastDTheta)/2;
# again, second
my $lastDDTheta = -sin($lastTheta * pi/180) * $scaling;
$lastDTheta = $midDTheta + ($midDDTheta + $lastDDTheta)/2;
$lastTheta = $midTheta + ($midDTheta + $lastDTheta)/2;
# Now put the values back in our globals
$dTheta = $lastDTheta;
$Theta = $lastTheta;
}
sub animate {
recompute_angle;
show_pendulum;
$after_id = $root->after(15 => sub {animate() });
}
show_pendulum;
$after_id = $root->after(500 => sub {animate});
$canvas->bind('<Destroy>' => sub {$after_id->cancel});
MainLoop;</syntaxhighlight>
=={{header|Phix}}==
{{libheader|Phix/pGUI}}
{{libheader|Phix/online}}
You can run this online [http://phix.x10.mx/p2js/animate_pendulum2.htm here].
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #000080;font-style:italic;">--
-- demo\rosetta\animate_pendulum.exw
-- =================================
--
-- Author Pete Lomax, March 2017
--
-- Port of animate_pendulum.exw from arwen to pGUI, which is now
-- preserved as a comment below (in the distro version only).
--
-- With help from lesterb, updates now in timer_cb not redraw_cb,
-- variables better named, and velocity problem sorted, July 2018.
--</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">full</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">false</span> <span style="color: #000080;font-style:italic;">-- set true for full swing to near-vertical.
-- false performs swing to horizontal only.
-- (adjusts the starting angle, pivot point,
-- and canvas size, only.)</span>
<span style="color: #008080;">include</span> <span style="color: #000000;">pGUI</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
<span style="color: #004080;">Ihandle</span> <span style="color: #000000;">dlg</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">canvas</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">timer</span>
<span style="color: #004080;">cdCanvas</span> <span style="color: #000000;">cdcanvas</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">g</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">50</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">angle</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">full</span><span style="color: #0000FF;">?</span><span style="color: #004600;">PI</span><span style="color: #0000FF;">-</span><span style="color: #000000;">0.01</span><span style="color: #0000FF;">:</span><span style="color: #004600;">PI</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">),</span> <span style="color: #000080;font-style:italic;">-- (near_vertical | horiz)</span>
<span style="color: #000000;">velocity</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">w</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">h</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">len</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">redraw_cb</span><span style="color: #0000FF;">(</span><span style="color: #004080;">Ihandle</span> <span style="color: #000080;font-style:italic;">/*ih*/</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000080;font-style:italic;">/*posx*/</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">/*posy*/</span><span style="color: #0000FF;">)</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">w</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">h</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">IupGetIntInt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">canvas</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"DRAWSIZE"</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">cdCanvasActivate</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cdcanvas</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">cdCanvasClear</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cdcanvas</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">-- new suspension point:</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">sX</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">w</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">sY</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h</span><span style="color: #0000FF;">/</span><span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">full</span><span style="color: #0000FF;">?</span><span style="color: #000000;">2</span><span style="color: #0000FF;">:</span><span style="color: #000000;">16</span><span style="color: #0000FF;">))</span> <span style="color: #000080;font-style:italic;">-- (mid | top)
-- repaint:</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">eX</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">len</span><span style="color: #0000FF;">*</span><span style="color: #7060A8;">sin</span><span style="color: #0000FF;">(</span><span style="color: #000000;">angle</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">sX</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">eY</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">len</span><span style="color: #0000FF;">*</span><span style="color: #7060A8;">cos</span><span style="color: #0000FF;">(</span><span style="color: #000000;">angle</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">sY</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">cdCanvasSetForeground</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cdcanvas</span><span style="color: #0000FF;">,</span> <span style="color: #004600;">CD_CYAN</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">cdCanvasLine</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cdcanvas</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">sX</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">h</span><span style="color: #0000FF;">-</span><span style="color: #000000;">sY</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">eX</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">h</span><span style="color: #0000FF;">-</span><span style="color: #000000;">eY</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">cdCanvasSetForeground</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cdcanvas</span><span style="color: #0000FF;">,</span> <span style="color: #004600;">CD_DARK_GREEN</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">cdCanvasSector</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cdcanvas</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">sX</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">h</span><span style="color: #0000FF;">-</span><span style="color: #000000;">sY</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">360</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">cdCanvasSetForeground</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cdcanvas</span><span style="color: #0000FF;">,</span> <span style="color: #004600;">CD_BLUE</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">cdCanvasSector</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cdcanvas</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">eX</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">h</span><span style="color: #0000FF;">-</span><span style="color: #000000;">eY</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">35</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">35</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">360</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">cdCanvasFlush</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cdcanvas</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #004600;">IUP_DEFAULT</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">timer_cb</span><span style="color: #0000FF;">(</span><span style="color: #004080;">Ihandle</span> <span style="color: #000080;font-style:italic;">/*ih*/</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">w</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">newlen</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">w</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)-</span><span style="color: #000000;">30</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">newlen</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">len</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">len</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">newlen</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">tmp</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">*</span><span style="color: #000000;">g</span><span style="color: #0000FF;">*</span><span style="color: #000000;">len</span><span style="color: #0000FF;">*(</span><span style="color: #7060A8;">cos</span><span style="color: #0000FF;">(</span><span style="color: #000000;">angle</span><span style="color: #0000FF;">))</span>
<span style="color: #000000;">velocity</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tmp</span><span style="color: #0000FF;"><</span><span style="color: #000000;">0</span><span style="color: #0000FF;">?</span><span style="color: #000000;">0</span><span style="color: #0000FF;">:</span><span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tmp</span><span style="color: #0000FF;">)*</span><span style="color: #7060A8;">sign</span><span style="color: #0000FF;">(</span><span style="color: #000000;">velocity</span><span style="color: #0000FF;">))</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">dt</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0.2</span><span style="color: #0000FF;">/</span><span style="color: #000000;">w</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">acceleration</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">len</span><span style="color: #0000FF;">*</span><span style="color: #7060A8;">sin</span><span style="color: #0000FF;">(</span><span style="color: #000000;">angle</span><span style="color: #0000FF;">)*</span><span style="color: #000000;">g</span>
<span style="color: #000000;">velocity</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">dt</span><span style="color: #0000FF;">*</span><span style="color: #000000;">acceleration</span>
<span style="color: #000000;">angle</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">dt</span><span style="color: #0000FF;">*</span><span style="color: #000000;">velocity</span>
<span style="color: #7060A8;">IupUpdate</span><span style="color: #0000FF;">(</span><span style="color: #000000;">canvas</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">return</span> <span style="color: #004600;">IUP_IGNORE</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">map_cb</span><span style="color: #0000FF;">(</span><span style="color: #004080;">Ihandle</span> <span style="color: #000000;">ih</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">IupGetDouble</span><span style="color: #0000FF;">(</span><span style="color: #004600;">NULL</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"SCREENDPI"</span><span style="color: #0000FF;">)/</span><span style="color: #000000;">25.4</span>
<span style="color: #7060A8;">IupGLMakeCurrent</span><span style="color: #0000FF;">(</span><span style="color: #000000;">canvas</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">platform</span><span style="color: #0000FF;">()=</span><span style="color: #004600;">JS</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">cdcanvas</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">cdCreateCanvas</span><span style="color: #0000FF;">(</span><span style="color: #004600;">CD_IUP</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">canvas</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">else</span>
<span style="color: #000000;">cdcanvas</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">cdCreateCanvas</span><span style="color: #0000FF;">(</span><span style="color: #004600;">CD_GL</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"10x10 %g"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">res</span><span style="color: #0000FF;">})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #7060A8;">cdCanvasSetBackground</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cdcanvas</span><span style="color: #0000FF;">,</span> <span style="color: #004600;">CD_PARCHMENT</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #004600;">IUP_DEFAULT</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">canvas_resize_cb</span><span style="color: #0000FF;">(</span><span style="color: #004080;">Ihandle</span> <span style="color: #000080;font-style:italic;">/*canvas*/</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">canvas_width</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">canvas_height</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">IupGetIntInt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">canvas</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"DRAWSIZE"</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">IupGetDouble</span><span style="color: #0000FF;">(</span><span style="color: #004600;">NULL</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"SCREENDPI"</span><span style="color: #0000FF;">)/</span><span style="color: #000000;">25.4</span>
<span style="color: #7060A8;">cdCanvasSetAttribute</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cdcanvas</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"SIZE"</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"%dx%d %g"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">canvas_width</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">canvas_height</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">})</span>
<span style="color: #008080;">return</span> <span style="color: #004600;">IUP_DEFAULT</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">main</span><span style="color: #0000FF;">()</span>
<span style="color: #7060A8;">IupOpen</span><span style="color: #0000FF;">()</span>
<span style="color: #000000;">canvas</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">IupGLCanvas</span><span style="color: #0000FF;">()</span>
<span style="color: #7060A8;">IupSetAttribute</span><span style="color: #0000FF;">(</span><span style="color: #000000;">canvas</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"RASTERSIZE"</span><span style="color: #0000FF;">,</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">full</span><span style="color: #0000FF;">?</span><span style="color: #008000;">"640x640"</span><span style="color: #0000FF;">:</span><span style="color: #008000;">"640x340"</span><span style="color: #0000FF;">))</span> <span style="color: #000080;font-style:italic;">-- (fit 360|180)</span>
<span style="color: #7060A8;">IupSetCallback</span><span style="color: #0000FF;">(</span><span style="color: #000000;">canvas</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"MAP_CB"</span><span style="color: #0000FF;">,</span> <span style="color: #7060A8;">Icallback</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"map_cb"</span><span style="color: #0000FF;">))</span>
<span style="color: #7060A8;">IupSetCallback</span><span style="color: #0000FF;">(</span><span style="color: #000000;">canvas</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"ACTION"</span><span style="color: #0000FF;">,</span> <span style="color: #7060A8;">Icallback</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"redraw_cb"</span><span style="color: #0000FF;">))</span>
<span style="color: #7060A8;">IupSetCallback</span><span style="color: #0000FF;">(</span><span style="color: #000000;">canvas</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"RESIZE_CB"</span><span style="color: #0000FF;">,</span> <span style="color: #7060A8;">Icallback</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"canvas_resize_cb"</span><span style="color: #0000FF;">))</span>
<span style="color: #000000;">timer</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">IupTimer</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">Icallback</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"timer_cb"</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">20</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">dlg</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">IupDialog</span><span style="color: #0000FF;">(</span><span style="color: #000000;">canvas</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">IupSetAttribute</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dlg</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"TITLE"</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"Animated Pendulum"</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">IupShow</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dlg</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">IupSetAttribute</span><span style="color: #0000FF;">(</span><span style="color: #000000;">canvas</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"RASTERSIZE"</span><span style="color: #0000FF;">,</span> <span style="color: #004600;">NULL</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">platform</span><span style="color: #0000FF;">()!=</span><span style="color: #004600;">JS</span> <span style="color: #008080;">then</span>
<span style="color: #7060A8;">IupMainLoop</span><span style="color: #0000FF;">()</span>
<span style="color: #7060A8;">IupClose</span><span style="color: #0000FF;">()</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #000000;">main</span><span style="color: #0000FF;">()</span>
<!--</syntaxhighlight>-->
=={{header|PicoLisp}}==
A minimalist solution. The pendulum consists of the center point '+', and the swinging xterm cursor.
<syntaxhighlight lang="picolisp">(load "@lib/math.l")
(de pendulum (X Y Len)
(let (Angle pi/2 V 0)
(call 'clear)
(call 'tput "cup" Y X)
(prin '+)
(call 'tput "cup" 1 (+ X Len))
(until (key 25) # 25 ms
(let A (*/ (sin Angle) -9.81 1.0)
(inc 'V (*/ A 40)) # DT = 25 ms = 1/40 sec
(inc 'Angle (*/ V 40)) )
(call 'tput "cup"
(+ Y (*/ Len (cos Angle) 2.2)) # Compensate for aspect ratio
(+ X (*/ Len (sin Angle) 1.0)) ) ) ) )</syntaxhighlight>
Test (hit any key to stop):
<syntaxhighlight lang="picolisp">(pendulum 40 1 36)</syntaxhighlight>
=={{header|Portugol}}==
{{trans|FreeBASIC}}
<syntaxhighlight lang="portugol">
programa {
inclua biblioteca Matematica --> math // math library
inclua biblioteca Util --> u // util library
inclua biblioteca Graficos --> g // graphics library
inclua biblioteca Teclado --> t // keyboard library
real accel, bx, by
real theta = math.PI * 0.5
real g = 9.81
real l = 1.0
real speed = 0.0
real px = 320.0
real py = 10.0
inteiro w = 10 // circle width and height (radius)
// main entry
funcao inicio() {
g.iniciar_modo_grafico(verdadeiro)
g.definir_dimensoes_janela(640, 400)
// while ESC key not pressed
enquanto (nao t.tecla_pressionada(t.TECLA_ESC)) {
bx = px + l * 300.0 * math.seno(theta)
by = py - l * 300.0 * math.cosseno(theta)
g.definir_cor(g.COR_PRETO)
g.limpar()
g.definir_cor(g.COR_BRANCO)
g.desenhar_linha(px, py, bx, by)
g.desenhar_elipse(bx - w, by - w, w * 2, w * 2, verdadeiro)
accel = g * math.seno(theta) / l / 100.0
speed = speed + accel / 100.0
theta = theta + speed
g.desenhar_texto(0, 370, "Pendulum")
g.desenhar_texto(0, 385, "Press ESC to quit")
g.renderizar()
u.aguarde(10)
}
}
}
</syntaxhighlight>
=={{header|Prolog}}==
SWI-Prolog has a graphic interface XPCE.
<syntaxhighlight lang="prolog">:- use_module(library(pce)).
pendulum :-
new(D, window('Pendulum')),
send(D, size, size(560, 300)),
new(Line, line(80, 50, 480, 50)),
send(D, display, Line),
new(Circle, circle(20)),
send(Circle, fill_pattern, colour(@default, 0, 0, 0)),
new(Boule, circle(60)),
send(Boule, fill_pattern, colour(@default, 0, 0, 0)),
send(D, display, Circle, point(270,40)),
send(Circle, handle, handle(h/2, w/2, in)),
send(Boule, handle, handle(h/2, w/2, out)),
send(Circle, connect, Boule, link(in, out, line(0,0,0,0,none))),
new(Anim, animation(D, 0.0, Boule, 200.0)),
send(D, done_message, and(message(Anim, free),
message(Boule, free),
message(Circle, free),
message(@receiver,destroy))),
send(Anim?mytimer, start),
send(D, open).
:- pce_begin_class(animation(window, angle, boule, len_pendulum), object).
variable(window, object, both, "Display window").
variable(boule, object, both, "bowl of the pendulum").
variable(len_pendulum, object, both, "len of the pendulum").
variable(angle, object, both, "angle with the horizontal").
variable(delta, object, both, "increment of the angle").
variable(mytimer, timer, both, "timer of the animation").
initialise(P, W:object, A:object, B : object, L:object) :->
"Creation of the object"::
send(P, window, W),
send(P, angle, A),
send(P, boule, B),
send(P, len_pendulum, L),
send(P, delta, 0.01),
send(P, mytimer, new(_, timer(0.01,message(P, anim_message)))).
% method called when the object is destroyed
% first the timer is stopped
% then all the resources are freed
unlink(P) :->
send(P?mytimer, stop),
send(P, send_super, unlink).
% message processed by the timer
anim_message(P) :->
get(P, angle, A),
get(P, len_pendulum, L),
calc(A, L, X, Y),
get(P, window, W),
get(P, boule, B),
send(W, display, B, point(X,Y)),
% computation of the next position
get(P, delta, D),
next_Angle(A, D, NA, ND),
send(P, angle, NA),
send(P, delta, ND).
:- pce_end_class.
% computation of the position of the bowl.
calc(Ang, Len, X, Y) :-
X is Len * cos(Ang)+ 250,
Y is Len * sin(Ang) + 20.
% computation of the next angle
% if we reach 0 or pi, delta change.
next_Angle(A, D, NA, ND) :-
NA is D + A,
(((D > 0, abs(pi-NA) < 0.01); (D < 0, abs(NA) < 0.01))->
ND = - D;
ND = D).
</syntaxhighlight>
=={{header|PureBasic}}==
If the code was part of a larger application it could be improved by specifying constants for the locations of image elements.
<syntaxhighlight lang="purebasic">Procedure handleError(x, msg.s)
If Not x
MessageRequester("Error", msg)
End
EndIf
EndProcedure
#ScreenW = 320
#ScreenH = 210
handleError(OpenWindow(0, 0, 0, #ScreenW, #ScreenH, "Animated Pendulum", #PB_Window_SystemMenu), "Can't open window.")
handleError(InitSprite(), "Can't setup sprite display.")
handleError(OpenWindowedScreen(WindowID(0), 0, 0, #ScreenW, #ScreenH, 0, 0, 0), "Can't open screen.")
Enumeration ;sprites
#bob_spr
#ceiling_spr
#pivot_spr
EndEnumeration
TransparentSpriteColor(#PB_Default, RGB(255, 0, 255))
CreateSprite(#bob_spr, 32, 32)
StartDrawing(SpriteOutput(#bob_spr))
Box(0, 0, 32, 32, RGB(255, 0, 255))
Circle(16, 16, 15, RGB(253, 252, 3))
DrawingMode(#PB_2DDrawing_Outlined)
Circle(16, 16, 15, RGB(0, 0, 0))
StopDrawing()
CreateSprite(#pivot_spr, 10, 10)
StartDrawing(SpriteOutput(#pivot_spr))
Box(0, 0, 10, 10, RGB(255, 0, 255))
Circle(5, 5, 4, RGB(125, 125, 125))
DrawingMode(#PB_2DDrawing_Outlined)
Circle(5, 5, 4, RGB(0,0 , 0))
StopDrawing()
CreateSprite(#ceiling_spr,#ScreenW,2)
StartDrawing(SpriteOutput(#ceiling_spr))
Box(0,0,SpriteWidth(#ceiling_spr), SpriteHeight(#ceiling_spr), RGB(126, 126, 126))
StopDrawing()
Structure pendulum
length.d ; meters
constant.d ; -g/l
gravity.d ; m/s²
angle.d ; radians
velocity.d ; m/s
EndStructure
Procedure initPendulum(*pendulum.pendulum, length.d = 1.0, gravity.d = 9.81, initialAngle.d = #PI / 2)
With *pendulum
\length = length
\gravity = gravity
\angle = initialAngle
\constant = -gravity / length
\velocity = 0.0
EndWith
EndProcedure
Procedure updatePendulum(*pendulum.pendulum, deltaTime.d)
deltaTime = deltaTime / 1000.0 ;ms
Protected acceleration.d = *pendulum\constant * Sin(*pendulum\angle)
*pendulum\velocity + acceleration * deltaTime
*pendulum\angle + *pendulum\velocity * deltaTime
EndProcedure
Procedure drawBackground()
ClearScreen(RGB(190,190,190))
;draw ceiling
DisplaySprite(#ceiling_spr, 0, 47)
;draw pivot
DisplayTransparentSprite(#pivot_spr, 154,43) ;origin in upper-left
EndProcedure
Procedure drawPendulum(*pendulum.pendulum)
;draw rod
Protected x = *pendulum\length * 140 * Sin(*pendulum\angle) ;scale = 1 m/140 pixels
Protected y = *pendulum\length * 140 * Cos(*pendulum\angle)
StartDrawing(ScreenOutput())
LineXY(154 + 5,43 + 5, 154 + 5 + x, 43 + 5 + y) ;draw from pivot-center to bob-center, adjusting for origins
StopDrawing()
;draw bob
DisplayTransparentSprite(#bob_spr, 154 + 5 - 16 + x, 43 + 5 - 16 + y) ;adj for origin in upper-left
EndProcedure
Define pendulum.pendulum, event
initPendulum(pendulum)
drawPendulum(pendulum)
AddWindowTimer(0, 1, 50)
Repeat
event = WindowEvent()
Select event
Case #pb_event_timer
drawBackground()
Select EventTimer()
Case 1
updatePendulum(pendulum, 50)
drawPendulum(pendulum)
EndSelect
FlipBuffers()
Case #PB_Event_CloseWindow
Break
EndSelect
ForEver</syntaxhighlight>
=={{header|Python}}==
==={{libheader|pygame}}===
{{trans|C}}
<syntaxhighlight lang="python">import pygame, sys
from pygame.locals import *
from math import sin, cos, radians
pygame.init()
WINDOWSIZE = 250
TIMETICK = 100
BOBSIZE = 15
window = pygame.display.set_mode((WINDOWSIZE, WINDOWSIZE))
pygame.display.set_caption("Pendulum")
screen = pygame.display.get_surface()
screen.fill((255,255,255))
PIVOT = (WINDOWSIZE/2, WINDOWSIZE/10)
SWINGLENGTH = PIVOT[1]*4
class BobMass(pygame.sprite.Sprite):
def __init__(self):
pygame.sprite.Sprite.__init__(self)
self.theta = 45
self.dtheta = 0
self.rect = pygame.Rect(PIVOT[0]-SWINGLENGTH*cos(radians(self.theta)),
PIVOT[1]+SWINGLENGTH*sin(radians(self.theta)),
1,1)
self.draw()
def recomputeAngle(self):
scaling = 3000.0/(SWINGLENGTH**2)
firstDDtheta = -sin(radians(self.theta))*scaling
midDtheta = self.dtheta + firstDDtheta
midtheta = self.theta + (self.dtheta + midDtheta)/2.0
midDDtheta = -sin(radians(midtheta))*scaling
midDtheta = self.dtheta + (firstDDtheta + midDDtheta)/2
midtheta = self.theta + (self.dtheta + midDtheta)/2
midDDtheta = -sin(radians(midtheta)) * scaling
lastDtheta = midDtheta + midDDtheta
lasttheta = midtheta + (midDtheta + lastDtheta)/2.0
lastDDtheta = -sin(radians(lasttheta)) * scaling
lastDtheta = midDtheta + (midDDtheta + lastDDtheta)/2.0
lasttheta = midtheta + (midDtheta + lastDtheta)/2.0
self.dtheta = lastDtheta
self.theta = lasttheta
self.rect = pygame.Rect(PIVOT[0]-
SWINGLENGTH*sin(radians(self.theta)),
PIVOT[1]+
SWINGLENGTH*cos(radians(self.theta)),1,1)
def draw(self):
pygame.draw.circle(screen, (0,0,0), PIVOT, 5, 0)
pygame.draw.circle(screen, (0,0,0), self.rect.center, BOBSIZE, 0)
pygame.draw.aaline(screen, (0,0,0), PIVOT, self.rect.center)
pygame.draw.line(screen, (0,0,0), (0, PIVOT[1]), (WINDOWSIZE, PIVOT[1]))
def update(self):
self.recomputeAngle()
screen.fill((255,255,255))
self.draw()
bob = BobMass()
TICK = USEREVENT + 2
pygame.time.set_timer(TICK, TIMETICK)
def input(events):
for event in events:
if event.type == QUIT:
sys.exit(0)
elif event.type == TICK:
bob.update()
while True:
input(pygame.event.get())
pygame.display.flip()</syntaxhighlight>
===Python: using tkinter===
<syntaxhighlight lang="python">
''' Python 3.6.5 code using Tkinter graphical user interface.'''
from tkinter import *
import math
class Animation:
def __init__(self, gw):
self.window = gw
self.xoff, self.yoff = 300, 100
self.angle = 0
self.sina = math.sin(self.angle)
self.cosa = math.cos(self.angle)
self.rodhyp = 170
self.bobr = 30
self.bobhyp = self.rodhyp + self.bobr
self.rodx0, self.rody0 = self.xoff, self.yoff
self.ra = self.rodx0
self.rb = self.rody0
self.rc = self.xoff + self.rodhyp*self.sina
self.rd = self.yoff + self.rodhyp*self.cosa
self.ba = self.xoff - self.bobr + self.bobhyp*self.sina
self.bb = self.yoff - self.bobr + self.bobhyp*self.cosa
self.bc = self.xoff + self.bobr + self.bobhyp*self.sina
self.bd = self.yoff + self.bobr + self.bobhyp*self.cosa
self.da = math.pi / 360
# create / fill canvas:
self.cnv = Canvas(gw, bg='lemon chiffon')
self.cnv.pack(fill=BOTH, expand=True)
self.cnv.create_line(0, 100, 600, 100,
fill='dodger blue',
width=3)
radius = 8
self.cnv.create_oval(300-radius, 100-radius,
300+radius, 100+radius,
fill='navy')
self.bob = self.cnv.create_oval(self.ba,
self.bb,
self.bc,
self.bd,
fill='red',
width=2)
self.rod = self.cnv.create_line(self.ra,
self.rb,
self.rc,
self.rd,
fill='dodger blue',
width=6)
self.animate()
def animate(self):
if abs(self.angle) > math.pi / 2:
self.da = - self.da
self.angle += self.da
self.sina = math.sin(self.angle)
self.cosa = math.cos(self.angle)
self.ra = self.rodx0
self.rb = self.rody0
self.rc = self.xoff + self.rodhyp*self.sina
self.rd = self.yoff + self.rodhyp*self.cosa
self.ba = self.xoff - self.bobr + self.bobhyp*self.sina
self.bb = self.yoff - self.bobr + self.bobhyp*self.cosa
self.bc = self.xoff + self.bobr + self.bobhyp*self.sina
self.bd = self.yoff + self.bobr + self.bobhyp*self.cosa
self.cnv.coords(self.rod,
self.ra,
self.rb,
self.rc,
self.rd)
self.cnv.coords(self.bob,
self.ba,
self.bb,
self.bc,
self.bd)
self.window.update()
self.cnv.after(5, self.animate)
root = Tk()
root.title('Pendulum')
root.geometry('600x400+100+50')
root.resizable(False, False)
a = Animation(root)
root.mainloop()
</syntaxhighlight>
=={{header|QB64}}==
<syntaxhighlight lang="qbasic">'declare and initialize variables
CONST PI = 3.141592
DIM SHARED Bob_X, Bob_Y, Pivot_X, Pivot_Y, Rod_Length, Rod_Angle, Bob_Angular_Acceleration, Bob_Angular_Velocity, Delta_Time, Drawing_Scale, G AS DOUBLE
DIM SHARED exit_flag AS INTEGER
'set gravity to Earth's by default (in m/s squared)
G = -9.80665
'set the pivot at the screen center near the top. Positions are in meters not pixels, and they translate to 320 and 60 pixels
Pivot_X = 1.6
Pivot_Y = 0.3
'set the rod length, 0.994 meters by default (gives 1 second period in Earth gravity)
Rod_Length = 0.994
'set the initial rod angle to 6 degrees and convert to radians. 6 degrees seems small but it is near to what clocks use so it
'makes the pendulum look like a clock's. More amplitude works perfectly but looks silly.
Rod_Angle = 6 * (PI / 180)
'set delta time, seconds. 5 miliseconds is precise enough.
Delta_Time = 0.05
'because the positions are calculated in meters, the pendulum as drawn would be way too small (1 meter = 1 pixel),
'so a scale factor is introduced (1 meter = 200 pixels by default)
Drawing_Scale = 200
'initialize the screen to 640 x 480, 16 colors
SCREEN 12
'main loop
DO
'math to figure out what the pendulum is doing based on the initial conditions.
'first calculate the position of the bob's center based on the rod angle by using the sine and cosine functions for x and y coordinates
Bob_X = (Pivot_X + SIN(Rod_Angle) * Rod_Length)
Bob_Y = (Pivot_Y + COS(Rod_Angle) * Rod_Length)
'then based on the rod's last angle, length, and gravitational acceleration, calculate the angular acceleration
Bob_Angular_Acceleration = G / Rod_Length * SIN(Rod_Angle)
'integrate the angular acceleration over time to obtain angular velocity
Bob_Angular_Velocity = Bob_Angular_Velocity + (Bob_Angular_Acceleration * Delta_Time)
'integrate the angular velocity over time to obtain a new angle for the rod
Rod_Angle = Rod_Angle + (Bob_Angular_Velocity * Delta_Time)
'draw the user interface and pendulum position
'clear the screen before drawing the next frame of the animation
CLS
'print information
PRINT " Gravity: " + STR$(ABS(G)) + " m/sý, Rod Length: " + STR$(Rod_Length); " m"
LOCATE 25, 1
PRINT "+/- keys control rod length, numbers 1-5 select gravity, (1 Earth, 2 the Moon, 3 Mars, 4 more 5 less), Q to exit"
'draw the pivot
CIRCLE (Pivot_X * Drawing_Scale, Pivot_Y * Drawing_Scale), 5, 8
PAINT STEP(0, 0), 8, 8
'draw the bob
CIRCLE (Bob_X * Drawing_Scale, Bob_Y * Drawing_Scale), 20, 14
PAINT STEP(0, 0), 14, 14
'draw the rod
LINE (Pivot_X * Drawing_Scale, Pivot_Y * Drawing_Scale)-(Bob_X * Drawing_Scale, Bob_Y * Drawing_Scale), 14
'process input
SELECT CASE UCASE$(INKEY$)
CASE "+"
'lengthen rod
Rod_Length = Rod_Length + 0.01
CASE "-"
'shorten rod
Rod_Length = Rod_Length - 0.01
CASE "1"
'Earth G
G = -9.80665
CASE "2"
'Moon G
G = -1.62
CASE "3"
'Mars G
G = -3.721
CASE "4"
'More G
G = G + 0.1
CASE "5"
'Less G
G = G - 0.1
CASE "Q"
'exit on any other key
exit_flag = 1
END SELECT
'wait before drawing the next frame
_DELAY Delta_Time
'loop the animation until the user presses any key
LOOP UNTIL exit_flag = 1</syntaxhighlight>
=={{header|R}}==
<syntaxhighlight lang="r">library(DescTools)
pendulum<-function(length=5,radius=1,circle.color="white",bg.color="white"){
tseq = c(seq(0,pi,by=.1),seq(pi,0,by=-.1))
slow=.27;fast=.07
sseq = c(seq(slow,fast,length.out = length(tseq)/4),seq(fast,slow,length.out = length(tseq)/4),seq(slow,fast,length.out = length(tseq)/4),seq(fast,slow,length.out = length(tseq)/4))
plot(0,0,xlim=c((-length-radius)*1.2,(length+radius)*1.2),ylim=c((-length-radius)*1.2,0),xaxt="n",yaxt="n",xlab="",ylab="")
cat("Press Esc to end animation")
while(T){
for(i in 1:length(tseq)){
rect(par("usr")[1],par("usr")[3],par("usr")[2],par("usr")[4],col = bg.color)
abline(h=0,col="grey")
points(0,0)
DrawCircle((radius+length)*cos(tseq[i]),(radius+length)*-sin(tseq[i]),r.out=radius,col=circle.color)
lines(c(0,length*cos(tseq[i])),c(0,length*-sin(tseq[i])))
Sys.sleep(sseq[i])
}
}
}
pendulum(5,1,"gold","lightblue")</syntaxhighlight>
=={{header|Racket}}==
<syntaxhighlight lang="racket">
#lang racket
(require 2htdp/image 2htdp/universe)
(define (pendulum)
(define (accel θ) (- (sin θ)))
(define θ (/ pi 2.5))
(define θ′ 0)
(define θ′′ (accel (/ pi 2.5)))
(define (x θ) (+ 200 (* 150 (sin θ))))
(define (y θ) (* 150 (cos θ)))
(λ (n)
(define p-image (underlay/xy (add-line (empty-scene 400 200) 200 0 (x θ) (y θ) "black")
(- (x θ) 5) (- (y θ) 5) (circle 5 "solid" "blue")))
(set! θ (+ θ (* θ′ 0.04)))
(set! θ′ (+ θ′ (* (accel θ) 0.04)))
p-image))
(animate (pendulum))
</syntaxhighlight>
=={{header|Raku}}==
(formerly Perl 6)
{{works with|Rakudo|2018.09}}
Handles window resizing, modifies pendulum length and period as window height changes. May need to tweek $ppi scaling to get good looking animation.
<syntaxhighlight lang="raku" line>use SDL2::Raw;
use Cairo;
my $width = 1000;
my $height = 400;
SDL_Init(VIDEO);
my $window = SDL_CreateWindow(
'Pendulum - Raku',
SDL_WINDOWPOS_CENTERED_MASK,
SDL_WINDOWPOS_CENTERED_MASK,
$width, $height, RESIZABLE
);
my $render = SDL_CreateRenderer($window, -1, ACCELERATED +| PRESENTVSYNC);
my $bob = Cairo::Image.create( Cairo::FORMAT_ARGB32, 32, 32 );
given Cairo::Context.new($bob) {
my Cairo::Pattern::Gradient::Radial $sphere .=
create(13.3, 12.8, 3.2, 12.8, 12.8, 32);
$sphere.add_color_stop_rgba(0, 1, 1, .698, 1);
$sphere.add_color_stop_rgba(1, .623, .669, .144, 1);
.pattern($sphere);
.arc(16, 16, 15, 0, 2 * pi);
.fill;
$sphere.destroy;
}
my $bob_texture = SDL_CreateTexture(
$render, %PIXELFORMAT<ARGB8888>,
STATIC, 32, 32
);
SDL_UpdateTexture(
$bob_texture,
SDL_Rect.new(:x(0), :y(0), :w(32), :h(32)),
$bob.data, $bob.stride // 32
);
SDL_SetTextureBlendMode($bob_texture, 1);
SDL_SetRenderDrawBlendMode($render, 1);
my $event = SDL_Event.new;
my $now = now; # time
my $Θ = -π/3; # start angle
my $ppi = 500; # scale
my $g = -9.81; # accelaration of gravity
my $ax = $width/2; # anchor x
my $ay = 25; # anchor y
my $len = $height - 75; # 'rope' length
my $vel; # velocity
my $dt; # delta time
main: loop {
while SDL_PollEvent($event) {
my $casted_event = SDL_CastEvent($event);
given $casted_event {
when *.type == QUIT { last main }
when *.type == WINDOWEVENT {
if .event == 5 {
$width = .data1;
$height = .data2;
$ax = $width/2;
$len = $height - 75;
}
}
}
}
$dt = now - $now;
$now = now;
$vel += $g / $len * sin($Θ) * $ppi * $dt;
$Θ += $vel * $dt;
my $bx = $ax + sin($Θ) * $len;
my $by = $ay + cos($Θ) * $len;
SDL_SetRenderDrawColor($render, 255, 255, 255, 255);
SDL_RenderDrawLine($render, |($ax, $ay, $bx, $by)».round);
SDL_RenderCopy( $render, $bob_texture, Nil,
SDL_Rect.new($bx - 16, $by - 16, 32, 32)
);
SDL_RenderPresent($render);
SDL_SetRenderDrawColor($render, 0, 0, 0, 0);
SDL_RenderClear($render);
}
SDL_Quit();</syntaxhighlight>
=={{header|REXX}}==
{{trans|Ada}}
{{trans|ooRexx}}
<br>REXX doesn't have a portable graphics user interface (GUI), but
this version is similar to the '''Ada''' version and just
<br>displays the coordinates of the end of the pendulum.
<syntaxhighlight lang="rexx">/*REXX program displays the (x, y) coördinates (at the end of a swinging pendulum). */
parse arg cycles Plength theta . /*obtain optional argument from the CL.*/
if cycles=='' | cycles=="," then cycles= 60 /*Not specified? Then use the default.*/
if pLength=='' | pLength=="," then pLength= 10 /* " " " " " " */
if theta=='' | theta=="," then theta= 30 /* " " " " " " */
theta= theta / 180 * pi() /* 'cause that's the way Ada did it. */
was= time('R') /*obtain the current elapsed time (was)*/
g= -9.81 /*gravitation constant (for earth). */
speed= 0 /*velocity of the pendulum, now resting*/
do cycles; call delay 1/20 /*swing the pendulum a number of times.*/
now= time('E') /*obtain the current time (in seconds).*/
duration= now - was /*calculate duration since last cycle. */
acceleration= g / pLength * sin(theta) /*compute the pendulum acceleration. */
x= sin(theta) * pLength /*calculate X coördinate of pendulum.*/
y= cos(theta) * pLength /* " Y " " */
speed= speed + acceleration * duration /*calculate " speed " " */
theta= theta + speed * duration /* " " angle " " */
was= now /*save the elapsed time as it was then.*/
say right('X: ',20) fmt(x) right("Y: ", 10) fmt(y)
end /*cycles*/
exit 0 /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
fmt: procedure; parse arg z; return left('', z>=0)format(z, , digits() - 1) /*align#*/
pi: pi= 3.1415926535897932384626433832795028841971693993751058209749445923078; return pi
r2r: return arg(1) // (pi() * 2) /*normalize radians ──► a unit circle. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
cos: procedure; parse arg x; x=r2r(x); numeric fuzz min(6,digits()-3); z=1; _=1; x=x*x
p=z; do k=2 by 2; _=-_*x/(k*(k-1)); z=z+_; if z=p then leave; p=z; end; return z
/*──────────────────────────────────────────────────────────────────────────────────────*/
sin: procedure; parse arg x; x=r2r(x); _=x; numeric fuzz min(5, max(1,digits()-3)); q=x*x
z=x; do k=2 by 2 until p=z; p= z; _= -_*q/(k*k+k); z= z+_; end; return z</syntaxhighlight>
Programming note: the '''SIN''' and '''COS''' functions above are abridged versions.
{{out|output|text= when using the default inputs:}}
(Shown at three-quarter size.)
<pre style="font-size:75%">
X: 5.00000001 Y: 8.66025263
X: 4.99061349 Y: 8.66566514
X: 4.97243576 Y: 8.67610852
X: 4.93067038 Y: 8.69991317
X: 4.89012042 Y: 8.72276910
X: 4.82031857 Y: 8.76153587
X: 4.75801424 Y: 8.79552638
X: 4.68636431 Y: 8.83391049
X: 4.57361919 Y: 8.89280584
X: 4.48234416 Y: 8.93916001
X: 4.37986973 Y: 8.98981271
X: 4.22616556 Y: 9.06308553
X: 4.10234645 Y: 9.11979981
X: 3.92362587 Y: 9.19810621
X: 3.77927439 Y: 9.25835208
X: 3.62636710 Y: 9.31930574
X: 3.41031145 Y: 9.40051989
X: 3.23831928 Y: 9.46114623
X: 3.05856966 Y: 9.52077477
X: 2.80449093 Y: 9.59869639
X: 2.60777314 Y: 9.65399458
X: 2.33706050 Y: 9.72307536
X: 2.12566754 Y: 9.77146685
X: 1.90875333 Y: 9.81614357
X: 1.61409349 Y: 9.86887572
X: 1.38628040 Y: 9.90344528
X: 1.15474731 Y: 9.93310425
X: 0.83894984 Y: 9.96474604
X: 0.60607739 Y: 9.98161664
X: 0.28427382 Y: 9.99595857
X: 0.04337158 Y: 9.99990600
X: -0.19764981 Y: 9.99804656
X: -0.51465016 Y: 9.98674803
X: -0.75351685 Y: 9.97157018
X: -0.99032702 Y: 9.95084184
X: -1.29813435 Y: 9.91538447
X: -1.52787755 Y: 9.88259045
X: -1.82867021 Y: 9.83137708
X: -2.04809904 Y: 9.78801877
X: -2.26218023 Y: 9.74076694
X: -2.53465430 Y: 9.67344838
X: -2.73460510 Y: 9.61883856
X: -2.92771580 Y: 9.56182417
X: -3.17015942 Y: 9.48420212
X: -3.34611403 Y: 9.42356201
X: -3.51412189 Y: 9.36220839
X: -3.72485659 Y: 9.28037935
X: -3.87040178 Y: 9.22062834
X: -4.01043937 Y: 9.16058801
X: -4.18250467 Y: 9.08331710
X: -4.30172468 Y: 9.02746685
X: -4.44332328 Y: 8.95861981
X: -4.54135551 Y: 8.90932543
X: -4.63012036 Y: 8.86351916
X: -4.73113128 Y: 8.81001598
X: -4.79830022 Y: 8.77361372
X: -4.85610202 Y: 8.74175352
X: -4.91679319 Y: 8.70776227
X: -4.95266247 Y: 8.68741106
X: -4.98366742 Y: 8.66966173
</pre>
=={{header|Ring}}==
<syntaxhighlight lang="ring">
# Project : Animate a pendulum
load "guilib.ring"
load "stdlib.ring"
CounterMan = 1
paint = null
pi = 22/7
theta = pi/180*40
g = 9.81
l = 0.50
speed = 0
new qapp
{
win1 = new qwidget() {
setwindowtitle("Animate a pendulum")
setgeometry(100,100,800,600)
label1 = new qlabel(win1) {
setgeometry(10,10,800,600)
settext("")
}
new qpushbutton(win1) {
setgeometry(150,500,100,30)
settext("draw")
setclickevent("draw()")
}
TimerMan = new qtimer(win1)
{
setinterval(1000)
settimeoutevent("draw()")
start()
}
show()
}
exec()
}
func draw
p1 = new qpicture()
color = new qcolor() {
setrgb(0,0,255,255)
}
pen = new qpen() {
setcolor(color)
setwidth(1)
}
paint = new qpainter() {
begin(p1)
setpen(pen)
ptime()
endpaint()
}
label1 { setpicture(p1) show() }
return
func ptime()
TimerMan.start()
pPlaySleep()
sleep(0.1)
CounterMan++
if CounterMan = 20
TimerMan.stop()
ok
func pPlaySleep()
pendulum(theta, l)
pendulum(theta, l)
accel = - g * sin(theta) / l / 100
speed = speed + accel / 100
theta = theta + speed
func pendulum(a, l)
pivotx = 640
pivoty = 800
bobx = pivotx + l * 1000 * sin(a)
boby = pivoty - l * 1000 * cos(a)
paint.drawline(pivotx, pivoty, bobx, boby)
paint.drawellipse(bobx + 24 * sin(a), boby - 24 * cos(a), 24, 24)
</syntaxhighlight>
Output video:
[https://www.dropbox.com/s/j9usrmmdy9pajmp/CalmoSoftPendulum.avi?dl=0 Animate a pendulum]
=={{header|RLaB}}==
The plane pendulum motion is an interesting and easy problem
in which the facilities of RLaB for numerical computation and simulation
are easily accessible.
The parameters of the problem are <math>L</math>, the length of the arm,
and <math>g</math> the magnitude of the gravity.
We start with the mathematical transliteration of the problem.
We solve it in plane (2-D) in terms of <math>\theta</math> describing
the angle between the <math>z</math>-axis and the arm of the pendulum,
where the downwards direction is taken as positive.
The Newton equation of motion, which is a second-order non-linear
ordinary differential equation (ODE) reads
:<math>\ddot\theta = -\frac{g}{L} \sin \theta</math>
In our example, we will solve the problem as, so called,
initial value problem (IVP).
That is, we will specify that at the time ''t=0'' the pendulum was at rest <math>\dot\theta(0)=0</math>, extended at an angle <math>\theta(0)=0.523598776</math>
radians (equivalent to 30 degrees).
RLaB has the facilities to solve ODE IVP which are accessible through ''odeiv'' solver. This solver requires that the ODE be written as the first order differential equation,
:<math>\dot u = f(u) </math>
Here, we introduced a vector <math>u = [\theta, \dot\theta] = [u_1, u_2]</math>,
for which the original ODE reads
:<math>\dot\theta = \dot u_1 = u_2 = f_1(u)</math>
:<math>\ddot\theta = \dot u_2 = -\frac{g}{L} \sin \theta = -\frac{g}{L} \sin u_1 =f_2(u)</math>.
The RLaB script that solves the problem is
<syntaxhighlight lang="rlab">
//
// example: solve ODE for pendulum
//
// we first define the first derivative function for the solver
dudt = function(t, u, p)
{
// t-> time
// u->[theta, dtheta/dt ]
// p-> g/L, parameter
rval = zeros(2,1);
rval[1] = u[2];
rval[2] = -p[1] * sin(u[1]);
return rval;
};
// now we solve the problem
// physical parameters
L = 5; // (m), the length of the arm of the pendulum
p = mks.g / L; // RLaB has a built-in list 'mks' which contains large number of physical constants and conversion factors
T0 = 2*const.pi*sqrt(L/mks.g); // approximate period of the pendulum
// initial conditions
theta0 = 30; // degrees, initial angle of deflection of pendulum
u0 = [theta0*const.pi/180, 0]; // RLaB has a built-in list 'const' of mathematical constants.
// times at which we want solution
t = [0:4:1/64] * T0; // solve for 4 approximate periods with at time points spaced at T0/64
// prepare ODEIV solver
optsode = <<>>;
optsode.eabs = 1e-6; // relative error for step size
optsode.erel = 1e-6; // absolute error for step size
optsode.delta_t = 1e-6; // maximum dt that code is allowed
optsode.stdout = stderr(); // open the text console and in it print the results of each step of calculation
optsode.imethod = 5; // use method No. 5 from the odeiv toolkit, Runge-Kutta 8th order Prince-Dormand method
//optsode.phase_space = 0; // the solver returns [t, u1(t), u2(t)] which is default behavior
optsode.phase_space = 1; // the solver returns [t, u1(t), u2(t), d(u1)/dt(t), d(u2)/dt]
// solver do my bidding
y = odeiv(dudt, p, t, u0, optsode);
// Make an animation. We choose to use 'pgplot' rather then 'gnuplot' interface because the former is
// faster and thus less cache-demanding, while the latter can be very cache-demanding (it may slow your
// linux system quite down if one sends lots of plots for gnuplot to plot).
plwins (1); // we will use one pgplot-window
plwin(1); // plot to pgplot-window No. 1; necessary if using more than one pgplot window
plimits (-L,L, -1.25*L, 0.25*L);
xlabel ("x-coordinate");
ylabel ("z-coordinate");
plegend ("Arm");
for (i in 1:y.nr)
{
// plot a line between the pivot point at (0,0) and the current position of the pendulum
arm_line = [0,0; L*sin(y[i;2]), -L*cos(y[i;2])]; // this is because theta is between the arm and the z-coordinate
plot (arm_line);
sleep (0.1); // sleep 0.1 seconds between plots
}
</syntaxhighlight>
=={{header|Ruby}}==
==={{libheader|Ruby/Tk}}===
{{trans|Tcl}}
This does not have the window resizing handling that Tcl does --
I did not spend enough time in the docs to figure out
how to get the new window size out of the configuration event.
Of interest when running this pendulum side-by-side with the Tcl one:
the Tcl pendulum swings noticibly faster.
<
$root = TkRoot.new("title" => "Pendulum Animation")
Line 345 ⟶ 4,671:
$canvas.bind('<Destroy>') {$root.after_cancel($after_id)}
Tk.mainloop</
==={{libheader|Shoes}}===
<syntaxhighlight lang="ruby">Shoes.app(:width => 320, :height => 200) do
@centerX = 160
@centerY = 25
@length = 150
@diameter = 15
@Theta = 45.0
@dTheta = 0.0
stroke gray
strokewidth 3
line 0,25,320,25
oval 155,20,10
stroke black
@rod = line(@centerX, @centerY, @centerX, @centerY + @length)
@bob = oval(@centerX - @diameter, @centerY + @length - @diameter, 2*@diameter)
animate(24) do |i|
recompute_angle
show_pendulum
end
def show_pendulum
angle = (90 + @Theta) * Math::PI / 180
x = @centerX + (Math.cos(angle) * @length).to_i
y = @centerY + (Math.sin(angle) * @length).to_i
@rod.remove
strokewidth 3
@rod = line(@centerX, @centerY, x, y)
@bob.move(x-@diameter, y-@diameter)
end
def recompute_angle
scaling = 3000.0 / (@length **2)
# first estimate
firstDDTheta = -Math.sin(@Theta * Math::PI / 180) * scaling
midDTheta = @dTheta + firstDDTheta
midTheta = @Theta + (@dTheta + midDTheta)/2
# second estimate
midDDTheta = -Math.sin(midTheta * Math::PI / 180) * scaling
midDTheta = @dTheta + (firstDDTheta + midDDTheta)/2
midTheta = @Theta + (@dTheta + midDTheta)/2
# again, first
midDDTheta = -Math.sin(midTheta * Math::PI / 180) * scaling
lastDTheta = midDTheta + midDDTheta
lastTheta = midTheta + (midDTheta + lastDTheta)/2
# again, second
lastDDTheta = -Math.sin(lastTheta * Math::PI/180) * scaling
lastDTheta = midDTheta + (midDDTheta + lastDDTheta)/2
lastTheta = midTheta + (midDTheta + lastDTheta)/2
# Now put the values back in our globals
@dTheta = lastDTheta
@Theta = lastTheta
end
end</syntaxhighlight>
==={{libheader|Ruby/Gosu}}===
<syntaxhighlight lang="ruby">#!/bin/ruby
begin; require 'rubygems'; rescue; end
require 'gosu'
include Gosu
# Screen size
W = 640
H = 480
# Full-screen mode
FS = false
# Screen update rate (Hz)
FPS = 60
class Pendulum
attr_accessor :theta, :friction
def initialize( win, x, y, length, radius, bob = true, friction = false)
@win = win
@centerX = x
@centerY = y
@length = length
@radius = radius
@bob = bob
@friction = friction
@theta = 60.0
@omega = 0.0
@scale = 2.0 / FPS
end
def draw
@win.translate(@centerX, @centerY) {
@win.rotate(@theta) {
@win.draw_quad(-1, 0, 0x3F_FF_FF_FF, 1, 0, 0x3F_FF_FF_00, 1, @length, 0x3F_FF_FF_00, -1, @length, 0x3F_FF_FF_FF )
if @bob
@win.translate(0, @length) {
@win.draw_quad(0, -@radius, Color::RED, @radius, 0, Color::BLUE, 0, @radius, Color::WHITE, -@radius, 0, Color::BLUE )
}
end
}
}
end
def update
# Thanks to Hugo Elias for the formula (and explanation thereof)
@theta += @omega
@omega = @omega - (Math.sin(@theta * Math::PI / 180) / (@length * @scale))
@theta *= 0.999 if @friction
end
end # Pendulum class
class GfxWindow < Window
def initialize
# Initialize the base class
super W, H, FS, 1.0 / FPS * 1000
# self.caption = "You're getting sleeeeepy..."
self.caption = "Ruby/Gosu Pendulum Simulator (Space toggles friction)"
@n = 1 # Try changing this number!
@pendulums = []
(1..@n).each do |i|
@pendulums.push Pendulum.new( self, W / 2, H / 10, H * 0.75 * (i / @n.to_f), H / 60 )
end
end
def draw
@pendulums.each { |pen| pen.draw }
end
def update
@pendulums.each { |pen| pen.update }
end
def button_up(id)
if id == KbSpace
@pendulums.each { |pen|
pen.friction = !pen.friction
pen.theta = (pen.theta <=> 0) * 45.0 unless pen.friction
}
else
close
end
end
def needs_cursor?()
true
end
end # GfxWindow class
begin
GfxWindow.new.show
rescue Exception => e
puts e.message, e.backtrace
gets
end</syntaxhighlight>
=={{header|Rust}}==
{{trans|C sharp}}
This is a translation of the C# code, albeit with a more explicit declaration of constants.
When moving the mouse over the viewport, the framerate accelerates somehow - any edits to keep the framerate constant is welcome!
{{libheader|piston_window}}
<syntaxhighlight lang="rust">
// using version 0.107.0 of piston_window
use piston_window::{clear, ellipse, line_from_to, PistonWindow, WindowSettings};
const PI: f64 = std::f64::consts::PI;
const WIDTH: u32 = 640;
const HEIGHT: u32 = 480;
const ANCHOR_X: f64 = WIDTH as f64 / 2. - 12.;
const ANCHOR_Y: f64 = HEIGHT as f64 / 4.;
const ANCHOR_ELLIPSE: [f64; 4] = [ANCHOR_X - 3., ANCHOR_Y - 3., 6., 6.];
const ROPE_ORIGIN: [f64; 2] = [ANCHOR_X, ANCHOR_Y];
const ROPE_LENGTH: f64 = 200.;
const ROPE_THICKNESS: f64 = 1.;
const DELTA: f64 = 0.05;
const STANDARD_GRAVITY_VALUE: f64 = -9.81;
// RGBA Colors
const BLACK: [f32; 4] = [0., 0., 0., 1.];
const RED: [f32; 4] = [1., 0., 0., 1.];
const GOLD: [f32; 4] = [216. / 255., 204. / 255., 36. / 255., 1.0];
fn main() {
let mut window: PistonWindow = WindowSettings::new("Pendulum", [WIDTH, HEIGHT])
.exit_on_esc(true)
.build()
.unwrap();
let mut angle = PI / 2.;
let mut angular_vel = 0.;
while let Some(event) = window.next() {
let (angle_sin, angle_cos) = angle.sin_cos();
let ball_x = ANCHOR_X + angle_sin * ROPE_LENGTH;
let ball_y = ANCHOR_Y + angle_cos * ROPE_LENGTH;
let angle_accel = STANDARD_GRAVITY_VALUE / ROPE_LENGTH * angle_sin;
angular_vel += angle_accel * DELTA;
angle += angular_vel * DELTA;
let rope_end = [ball_x, ball_y];
let ball_ellipse = [ball_x - 7., ball_y - 7., 14., 14.];
window.draw_2d(&event, |context, graphics, _device| {
clear([1.0; 4], graphics);
line_from_to(
BLACK,
ROPE_THICKNESS,
ROPE_ORIGIN,
rope_end,
context.transform,
graphics,
);
ellipse(RED, ANCHOR_ELLIPSE, context.transform, graphics);
ellipse(GOLD, ball_ellipse, context.transform, graphics);
});
}
}
</syntaxhighlight>
=={{header|Scala}}==
{{libheader|Scala}}
<syntaxhighlight lang="scala">import java.awt.Color
import java.util.concurrent.{Executors, TimeUnit}
import scala.swing.{Graphics2D, MainFrame, Panel, SimpleSwingApplication}
import scala.swing.Swing.pair2Dimension
object Pendulum extends SimpleSwingApplication {
val length = 100
lazy val ui = new Panel {
import scala.math.{cos, Pi, sin}
background = Color.white
preferredSize = (2 * length + 50, length / 2 * 3)
peer.setDoubleBuffered(true)
var angle: Double = Pi / 2
override def paintComponent(g: Graphics2D): Unit = {
super.paintComponent(g)
val (anchorX, anchorY) = (size.width / 2, size.height / 4)
val (ballX, ballY) =
(anchorX + (sin(angle) * length).toInt, anchorY + (cos(angle) * length).toInt)
g.setColor(Color.lightGray)
g.drawLine(anchorX - 2 * length, anchorY, anchorX + 2 * length, anchorY)
g.setColor(Color.black)
g.drawLine(anchorX, anchorY, ballX, ballY)
g.fillOval(anchorX - 3, anchorY - 4, 7, 7)
g.drawOval(ballX - 7, ballY - 7, 14, 14)
g.setColor(Color.yellow)
g.fillOval(ballX - 7, ballY - 7, 14, 14)
}
val animate: Runnable = new Runnable {
var angleVelocity = 0.0
var dt = 0.1
override def run(): Unit = {
angleVelocity += -9.81 / length * Math.sin(angle) * dt
angle += angleVelocity * dt
repaint()
}
}
}
override def top = new MainFrame {
title = "Rosetta Code >>> Task: Animate a pendulum | Language: Scala"
contents = ui
centerOnScreen()
Executors.
newSingleThreadScheduledExecutor().
scheduleAtFixedRate(ui.animate, 0, 15, TimeUnit.MILLISECONDS)
}
}</syntaxhighlight>
=={{header|Scheme}}==
{{libheader|Scheme/PsTk}}
{{trans|Ruby}}
This is a direct translation of the Ruby/Tk example into Scheme + PS/Tk.
<syntaxhighlight lang="scheme">#!r6rs
;;; R6RS implementation of Pendulum Animation
(import (rnrs)
(lib pstk main) ; change this for your pstk installation
)
(define PI 3.14159)
(define *conv-radians* (/ PI 180))
(define *theta* 45.0)
(define *d-theta* 0.0)
(define *length* 150)
(define *home-x* 160)
(define *home-y* 25)
;;; estimates new angle of pendulum
(define (recompute-angle)
(define (avg a b) (/ (+ a b) 2))
(let* ((scaling (/ 3000.0 (* *length* *length*)))
; first estimate
(first-dd-theta (- (* (sin (* *theta* *conv-radians*)) scaling)))
(mid-d-theta (+ *d-theta* first-dd-theta))
(mid-theta (+ *theta* (avg *d-theta* mid-d-theta)))
; second estimate
(mid-dd-theta (- (* (sin (* mid-theta *conv-radians*)) scaling)))
(mid-d-theta-2 (+ *d-theta* (avg first-dd-theta mid-dd-theta)))
(mid-theta-2 (+ *theta* (avg *d-theta* mid-d-theta-2)))
; again first
(mid-dd-theta-2 (- (* (sin (* mid-theta-2 *conv-radians*)) scaling)))
(last-d-theta (+ mid-d-theta-2 mid-dd-theta-2))
(last-theta (+ mid-theta-2 (avg mid-d-theta-2 last-d-theta)))
; again second
(last-dd-theta (- (* (sin (* last-theta *conv-radians*)) scaling)))
(last-d-theta-2 (+ mid-d-theta-2 (avg mid-dd-theta-2 last-dd-theta)))
(last-theta-2 (+ mid-theta-2 (avg mid-d-theta-2 last-d-theta-2))))
; put values back in globals
(set! *d-theta* last-d-theta-2)
(set! *theta* last-theta-2)))
;;; The main event loop and graphics context
(let ((tk (tk-start)))
(tk/wm 'title tk "Pendulum Animation")
(let ((canvas (tk 'create-widget 'canvas)))
;;; redraw the pendulum on canvas
;;; - uses angle and length to compute new (x,y) position of bob
(define (show-pendulum canvas)
(let* ((pendulum-angle (* *conv-radians* *theta*))
(x (+ *home-x* (* *length* (sin pendulum-angle))))
(y (+ *home-y* (* *length* (cos pendulum-angle)))))
(canvas 'coords 'rod *home-x* *home-y* x y)
(canvas 'coords 'bob (- x 15) (- y 15) (+ x 15) (+ y 15))))
;;; move the pendulum and repeat after 20ms
(define (animate)
(recompute-angle)
(show-pendulum canvas)
(tk/after 20 animate))
;; layout the canvas
(tk/grid canvas 'column: 0 'row: 0)
(canvas 'create 'line 0 25 320 25 'tags: 'plate 'width: 2 'fill: 'grey50)
(canvas 'create 'oval 155 20 165 30 'tags: 'pivot 'outline: "" 'fill: 'grey50)
(canvas 'create 'line 1 1 1 1 'tags: 'rod 'width: 3 'fill: 'black)
(canvas 'create 'oval 1 1 2 2 'tags: 'bob 'outline: 'black 'fill: 'yellow)
;; get everything started
(show-pendulum canvas)
(tk/after 500 animate)
(tk-event-loop tk)))
</syntaxhighlight>
Another version using gauche scheme:
<syntaxhighlight lang="scheme">
#!/usr/bin/env gosh
#| -*- mode: scheme; coding: utf-8; -*- |#
(use gl)
(use gl.glut)
(use gl.simple.viewer)
(use math.const)
(define (deg->rad degree) (* (/ degree 180) pi))
(define (rad->deg radians) (* (/ radians pi) 180))
(define (main args)
(glut-init args)
(let* ((φ (deg->rad 179)) (l 0.5) (bob 0.02) (q (make <glu-quadric>))
(draw-pendulum (lambda()
(gl-push-matrix*
(gl-scale 4 4 4)
(gl-translate 0 l 0)
(gl-rotate (rad->deg φ) 0 0 1)
(gl-begin GL_LINES)
(gl-vertex 0 0)
(gl-vertex 0 (- l))
(gl-end)
(gl-translate 0 (- l) 0)
(glu-sphere q bob 10 10))))
(g 9.81)
(φ̇ 0)
(euler-step (lambda(h)
(inc! φ̇ (* (- (* (/ g l) (sin φ))) h))
(inc! φ (* φ̇ h)))))
(simple-viewer-display
(lambda ()
;; I hope sync to VBLANK aka VSYNC works and the display has ~60Hz
(euler-step 1/60)
(draw-pendulum)
(glut-post-redisplay))))
(simple-viewer-window 'pendulum)
(glut-full-screen)
(simple-viewer-run :rescue-errors #f))
</syntaxhighlight>
=={{header|Scilab}}==
The animation is displayed on a graphic window, and won't stop until it shows all positions calculated unless the user abort the execution on Scilab console.
<syntaxhighlight lang="text">//Input variables (Assumptions: massless pivot, no energy loss)
bob_mass=10;
g=-9.81;
L=2;
theta0=-%pi/6;
v0=0;
t0=0;
//No. of steps
steps=300;
//Setting deltaT or duration (comment either of the lines below)
//deltaT=0.1; t_max=t0+deltaT*steps;
t_max=5; deltaT=(t_max-t0)/steps;
if t_max<=t0 then
error("Check duration (t0 and t_f), number of steps and deltaT.");
end
//Initial position
not_a_pendulum=%F;
t=zeros(1,steps); t(1)=t0; //time
theta=zeros(1,steps); theta(1)=theta0; //angle
F=zeros(1,steps); F(1)=bob_mass*g*sin(theta0); //force
A=zeros(1,steps); A(1)=F(1)/bob_mass; //acceleration
V=zeros(1,steps); V(1)=v0; //linear speed
W=zeros(1,steps); W(1)=v0/L; //angular speed
for i=2:steps
t(i)=t(i-1)+deltaT;
V(i)=A(i-1)*deltaT+V(i-1);
W(i)=V(i)/L;
theta(i)=theta(i-1)+W(i)*deltaT;
F(i)=bob_mass*g*sin(theta(i));
A(i)=F(i)/bob_mass;
if (abs(theta(i))>=%pi | (abs(theta(i))==0 & V(i)==0)) & ~not_a_pendulum then
disp("Initial conditions do not describe a pendulum.");
not_a_pendulum = %T;
end
end
clear i
//Ploting the pendulum
bob_r=0.08*L;
bob_shape=bob_r*exp(%i.*linspace(0,360,20)/180*%pi);
bob_pos=zeros(20,steps);
rod_pos=zeros(1,steps);
for i=1:steps
rod_pos(i)=L*exp(%i*(-%pi/2+theta(i)));
bob_pos(:,i)=bob_shape'+rod_pos(i);
end
clear i
scf(0); clf(); xname("Simple gravity pendulum");
plot2d(real([0 rod_pos(1)]),imag([0 rod_pos(1)]));
axes=gca();
axes.isoview="on";
axes.children(1).children.mark_style=3;
axes.children(1).children.mark_size=1;
axes.children(1).children.thickness=3;
plot2d(real(bob_pos(:,1)),imag(bob_pos(:,1)));
axes=gca();
axes.children(1).children.fill_mode="on";
axes.children(1).children.foreground=2;
axes.children(1).children.background=2;
if max(imag(bob_pos))>0 then
axes.data_bounds=[-L-bob_r,-L-1.01*bob_r;L+bob_r,max(imag(bob_pos))];
else
axes.data_bounds=[-L-bob_r,-L-1.01*bob_r;L+bob_r,bob_r];
end
//Animating the plot
disp("Duration: "+string(max(t)+deltaT-t0)+"s.");
sleep(850);
for i=2:steps
axes.children(1).children.data=[real(bob_pos(:,i)), imag(bob_pos(:,i))];
axes.children(2).children.data=[0, 0; real(rod_pos(i)), imag(rod_pos(i))];
sleep(deltaT*1000)
end
clear i</syntaxhighlight>
=={{header|SequenceL}}==
{{libheader|EaselSL}}
Using the [https://github.com/bethune-bryant/Easel Easel Engine for SequenceL] <br>
<syntaxhighlight lang="sequencel">import <Utilities/Sequence.sl>;
import <Utilities/Conversion.sl>;
import <Utilities/Math.sl>;
//region Types
Point ::= (x: int(0), y: int(0));
Color ::= (red: int(0), green: int(0), blue: int(0));
Image ::= (kind: char(1), iColor: Color(0), vert1: Point(0), vert2: Point(0), vert3: Point(0), center: Point(0),
radius: int(0), height: int(0), width: int(0), message: char(1), source: char(1));
Click ::= (clicked: bool(0), clPoint: Point(0));
Input ::= (iClick: Click(0), keys: char(1));
//endregion
//region Helpers======================================================================
//region Constructor-Functions-------------------------------------------------
point(a(0), b(0)) := (x: a, y: b);
color(r(0), g(0), b(0)) := (red: r, green: g, blue: b);
segment(e1(0), e2(0), c(0)) := (kind: "segment", vert1: e1, vert2: e2, iColor: c);
disc(ce(0), rad(0), c(0)) := (kind: "disc", center: ce, radius: rad, iColor: c);
//endregion----------------------------------------------------------------------
//region Colors----------------------------------------------------------------
dBlack := color(0, 0, 0);
dYellow := color(255, 255, 0);
//endregion----------------------------------------------------------------------
//endregion=============================================================================
//=================Easel=Functions=============================================
State ::= (angle: float(0), angleVelocity: float(0), angleAccel: float(0));
initialState := (angle: pi/2, angleVelocity: 0.0, angleAccel: 0.0);
dt := 0.3;
length := 450;
anchor := point(500, 750);
newState(I(0), S(0)) :=
let
newAngle := S.angle + newAngleVelocity * dt;
newAngleVelocity := S.angleVelocity + newAngleAccel * dt;
newAngleAccel := -9.81 / length * sin(S.angle);
in
(angle: newAngle, angleVelocity: newAngleVelocity, angleAccel: newAngleAccel);
sounds(I(0), S(0)) := ["ding"] when I.iClick.clicked else [];
images(S(0)) :=
let
pendulum := pendulumLocation(S.angle);
in
[segment(anchor, pendulum, dBlack),
disc(pendulum, 30, dYellow),
disc(anchor, 5, dBlack)];
pendulumLocation(angle) :=
let
x := anchor.x + round(sin(angle) * length);
y := anchor.y - round(cos(angle) * length);
in
point(x, y);
//=============End=Easel=Functions=============================================</syntaxhighlight>
{{out}}
[http://i.imgur.com/ZR2sK54.gifv GIF of Output]
=={{header|Sidef}}==
{{trans|Perl}}
<syntaxhighlight lang="ruby">require('Tk')
var root = %s<MainWindow>.new('-title' => 'Pendulum Animation')
var canvas = root.Canvas('-width' => 320, '-height' => 200)
canvas.createLine( 0, 25, 320, 25, '-tags' => <plate>, '-width' => 2, '-fill' => :grey50)
canvas.createOval(155, 20, 165, 30, '-tags' => <pivot outline>, '-fill' => :grey50)
canvas.createLine( 1, 1, 1, 1, '-tags' => <rod width>, '-width' => 3, '-fill' => :black)
canvas.createOval( 1, 1, 2, 2, '-tags' => <bob outline>, '-fill' => :yellow)
canvas.raise(:pivot)
canvas.pack('-fill' => :both, '-expand' => 1)
var(θ = 45, Δθ = 0, length = 150, homeX = 160, homeY = 25)
func show_pendulum() {
var angle = θ.deg2rad
var x = (homeX + length*sin(angle))
var y = (homeY + length*cos(angle))
canvas.coords(:rod, homeX, homeY, x, y)
canvas.coords(:bob, x - 15, y - 15, x + 15, y + 15)
}
func recompute_angle() {
var scaling = 3000/(length**2)
# first estimate
var firstΔΔθ = (-sin(θ.deg2rad) * scaling)
var midΔθ = (Δθ + firstΔΔθ)
var midθ = ((Δθ + midΔθ)/2 + θ)
# second estimate
var midΔΔθ = (-sin(midθ.deg2rad) * scaling)
midΔθ = ((firstΔΔθ + midΔΔθ)/2 + Δθ)
midθ = ((Δθ + midΔθ)/2 + θ)
# again, first
midΔΔθ = (-sin(midθ.deg2rad) * scaling)
var lastΔθ = (midΔθ + midΔΔθ)
var lastθ = ((midΔθ + lastΔθ)/2 + midθ)
# again, second
var lastΔΔθ = (-sin(lastθ.deg2rad) * scaling)
lastΔθ = ((midΔΔθ + lastΔΔθ)/2 + midΔθ)
lastθ = ((midΔθ + lastΔθ)/2 + midθ)
# Now put the values back in our globals
Δθ = lastΔθ
θ = lastθ
}
func animate(Ref id) {
recompute_angle()
show_pendulum()
*id = root.after(15 => { animate(id) })
}
show_pendulum()
var after_id = root.after(500 => { animate(\after_id) })
canvas.bind('<Destroy>' => { after_id.cancel })
%S<Tk>.MainLoop()</syntaxhighlight>
=={{header|smart BASIC}}==
<syntaxhighlight lang="smart basic">'Pendulum
'By Dutchman
' --- constants
g=9.81 ' accelleration of gravity
l=1 ' length of pendulum
GET SCREEN SIZE sw,sh
pivotx=sw/2
pivoty=150
' --- initialise graphics
GRAPHICS
DRAW COLOR 1,0,0
FILL COLOR 0,0,1
DRAW SIZE 2
' --- initialise pendulum
theta=1 ' initial displacement in radians
speed=0
' --- loop
DO
bobx=pivotx+100*l*SIN(theta)
boby=pivoty-100*l*COS(theta)
GOSUB Plot
PAUSE 0.01
accel=g*SIN(theta)/l/100
speed=speed+accel
theta=theta+speed
UNTIL 0
END
' --- subroutine
Plot:
REFRESH OFF
GRAPHICS CLEAR 1,1,0.5
DRAW LINE pivotx,pivoty TO bobx,boby
FILL CIRCLE bobx,boby SIZE 10
REFRESH ON
RETURN
</syntaxhighlight>
<pre>
We hope that the webmaster will soon have image uploads enabled again so that we can show a screen shot.
</pre>
=={{header|Tcl}}==
{{works with|Tcl|8.5
==={{libheader|Tk}}===
<syntaxhighlight lang="tcl">package require Tcl 8.5
package require Tk
Line 428 ⟶ 5,435:
bind .c <Configure> {resized %w}
# Callback to stop the animation cleanly when the GUI goes away
bind .c <Destroy> {after cancel $animation}</
=={{header|VBScript}}==
Well, VbScript does'nt have a graphics mode so this is a wobbly textmode pandulum. It should be called from cscript.
<syntaxhighlight lang="vb">
option explicit
const dt = 0.15
const length=23
dim ans0:ans0=chr(27)&"["
dim Veloc,Accel,angle,olr,olc,r,c
const r0=1
const c0=40
cls
angle=0.7
while 1
wscript.sleep(50)
Accel = -.9 * sin(Angle)
Veloc = Veloc + Accel * dt
Angle = Angle + Veloc * dt
r = r0 + int(cos(Angle) * Length)
c = c0+ int(2*sin(Angle) * Length)
cls
draw_line r,c,r0,c0
toxy r,c,"O"
olr=r :olc=c
wend
sub cls() wscript.StdOut.Write ans0 &"2J"&ans0 &"?25l":end sub
sub toxy(r,c,s) wscript.StdOut.Write ans0 & r & ";" & c & "f" & s :end sub
Sub draw_line(r1,c1, r2,c2) 'Bresenham's line drawing
Dim x,y,xf,yf,dx,dy,sx,sy,err,err2
x =r1 : y =c1
xf=r2 : yf=c2
dx=Abs(xf-x) : dy=Abs(yf-y)
If x<xf Then sx=+1: Else sx=-1
If y<yf Then sy=+1: Else sy=-1
err=dx-dy
Do
toxy x,y,"."
If x=xf And y=yf Then Exit Do
err2=err+err
If err2>-dy Then err=err-dy: x=x+sx
If err2< dx Then err=err+dx: y=y+sy
Loop
End Sub 'draw_line
</syntaxhighlight>
=={{header|Wren}}==
{{trans|Kotlin}}
{{libheader|DOME}}
{{libheader|Wren-dynamic}}
<syntaxhighlight lang="wren">import "graphics" for Canvas, Color
import "dome" for Window
import "math" for Math
import "./dynamic" for Tuple
var Element = Tuple.create("Element", ["x", "y"])
var Dt = 0.1
var Angle = Num.pi / 2
var AngleVelocity = 0
class Pendulum {
construct new(length) {
Window.title = "Pendulum"
_w = 2 * length + 50
_h = length / 2 * 3
Window.resize(_w, _h)
Canvas.resize(_w, _h)
_length = length
_anchor = Element.new((_w/2).floor, (_h/4).floor)
_fore = Color.black
}
init() {
drawPendulum()
}
drawPendulum() {
Canvas.cls(Color.white)
var ball = Element.new((_anchor.x + Math.sin(Angle) * _length).truncate,
(_anchor.y + Math.cos(Angle) * _length).truncate)
Canvas.line(_anchor.x, _anchor.y, ball.x, ball.y, _fore, 2)
Canvas.circlefill(_anchor.x - 3, _anchor.y - 4, 7, Color.lightgray)
Canvas.circle(_anchor.x - 3, _anchor.y - 4, 7, _fore)
Canvas.circlefill(ball.x - 7, ball.y - 7, 14, Color.yellow)
Canvas.circle(ball.x - 7, ball.y - 7, 14, _fore)
}
update() {
AngleVelocity = AngleVelocity - 9.81 / _length * Math.sin(Angle) * Dt
Angle = Angle + AngleVelocity * Dt
}
draw(alpha) {
drawPendulum()
}
}
var Game = Pendulum.new(200)</syntaxhighlight>
=={{header|XPL0}}==
<syntaxhighlight lang="xpl0">include c:\cxpl\codes; \intrinsic 'code' declarations
proc Ball(X0, Y0, R, C); \Draw a filled circle
int X0, Y0, R, C; \center coordinates, radius, color
int X, Y;
for Y:= -R to R do
for X:= -R to R do
if X*X + Y*Y <= R*R then Point(X+X0, Y+Y0, C);
def L = 2.0, \pendulum arm length (meters)
G = 9.81, \acceleration due to gravity (meters/second^2)
Pi = 3.14,
DT = 1.0/72.0; \delta time = screen refresh rate (seconds)
def X0=640/2, Y0=480/2; \anchor point = center coordinate
real S, V, A, T; \arc length, velocity, acceleration, theta angle
int X, Y; \ball coordinates
[SetVid($101); \set 640x480x8 graphic display mode
T:= Pi*0.75; V:= 0.0; \starting angle and velocity
S:= T*L;
repeat A:= -G*Sin(T);
V:= V + A*DT;
S:= S + V*DT;
T:= S/L;
X:= X0 + fix(L*100.0*Sin(T)); \100 scales to fit screen
Y:= Y0 + fix(L*100.0*Cos(T));
Move(X0, Y0); Line(X, Y, 7); \draw pendulum
Ball(X, Y, 10, $E\yellow\);
while port($3DA) & $08 do []; \wait for vertical retrace to go away
repeat until port($3DA) & $08; \wait for vertical retrace signal
Move(X0, Y0); Line(X, Y, 0); \erase pendulum
Ball(X, Y, 10, 0\black\);
until KeyHit; \keystroke terminates program
SetVid(3); \restore normal text screen
]</syntaxhighlight>
=={{header|Yabasic}}==
<syntaxhighlight lang="yabasic">clear screen
open window 400, 300
window origin "cc"
rodLen = 160
gravity = 2
damp = .989
TWO_PI = pi * 2
angle = 90 * 0.01745329251 // convert degree to radian
repeat
acceleration = -gravity / rodLen * sin(angle)
angle = angle + velocity : if angle > TWO_PI angle = 0
velocity = velocity + acceleration
velocity = velocity * damp
posX = sin(angle) * rodLen
posY = cos(angle) * rodLen - 70
clear window
text -50, -100, "Press 'q' to quit"
color 250, 0, 250
fill circle 0, -70, 4
line 0, -70, posX, posY
color 250, 100, 20
fill circle posX, posY, 10
until(lower$(inkey$(0.02)) = "q")
exit</syntaxhighlight>
=={{header|Zig}}==
{{libheader|Raylib}}
{{works with|Zig|0.11.0dev}} {{works with|Raylib|4.6dev}}
{{trans|Nim}}
<syntaxhighlight lang="zig">const math = @import("std").math;
const c = @cImport({
@cInclude("raylib.h");
});</syntaxhighlight>
<syntaxhighlight lang="zig">pub fn main() void {
c.SetConfigFlags(c.FLAG_VSYNC_HINT);
c.InitWindow(640, 320, "Pendulum");
defer c.CloseWindow();
// Simulation constants.
const g = 9.81; // Gravity (should be positive).
const length = 5.0; // Pendulum length.
const theta0 = math.pi / 3.0; // Initial angle for which omega = 0.
const e = g * length * (1 - @cos(theta0)); // Total energy = potential energy when starting.
// Simulation variables.
var theta: f32 = theta0; // Current angle.
var omega: f32 = 0; // Angular velocity = derivative of theta.
var accel: f32 = -g / length * @sin(theta0); // Angular acceleration = derivative of omega.
c.SetTargetFPS(60);
while (!c.WindowShouldClose()) // Detect window close button or ESC key
{
const half_width = @as(f32, @floatFromInt(c.GetScreenWidth())) / 2;
const pivot = c.Vector2{ .x = half_width, .y = 0 };
// Compute the position of the mass.
const mass = c.Vector2{
.x = 300 * @sin(theta) + pivot.x,
.y = 300 * @cos(theta),
};
{
c.BeginDrawing();
defer c.EndDrawing();
c.ClearBackground(c.RAYWHITE);
c.DrawLineV(pivot, mass, c.GRAY);
c.DrawCircleV(mass, 20, c.GRAY);
}
// Update theta and omega.
const dt = c.GetFrameTime();
theta += (omega + dt * accel / 2) * dt;
omega += accel * dt;
// If, due to computation errors, potential energy is greater than total energy,
// reset theta to ±theta0 and omega to 0.
if (length * g * (1 - @cos(theta)) >= e) {
theta = math.sign(theta) * theta0;
omega = 0;
}
accel = -g / length * @sin(theta);
}
}</syntaxhighlight>
=={{header|ZX Spectrum Basic}}==
{{trans|ERRE}}
In a real Spectrum it is too slow. Use the BasinC emulator/editor at maximum speed for realistic animation.
<syntaxhighlight lang="zxbasic">10 OVER 1: CLS
20 LET theta=1
30 LET g=9.81
40 LET l=0.5
50 LET speed=0
100 LET pivotx=120
110 LET pivoty=140
120 LET bobx=pivotx+l*100*SIN (theta)
130 LET boby=pivoty+l*100*COS (theta)
140 GO SUB 1000: PAUSE 1: GO SUB 1000
190 LET accel=g*SIN (theta)/l/100
200 LET speed=speed+accel/100
210 LET theta=theta+speed
220 GO TO 100
1000 PLOT pivotx,pivoty: DRAW bobx-pivotx,boby-pivoty
1010 CIRCLE bobx,boby,3
1020 RETURN</syntaxhighlight>
{{omit from|LFE}}
{{omit from|Maxima}}
{{omit from|PARI/GP}}
{{omit from|PHP}}
{{omit from|SQL PL|It does not handle GUI}}
| |||