Animate a pendulum

Animate a pendulum
You are encouraged to solve this task according to the task description, using any language you may know.

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 simple gravity pendulum.

For this task, create a simple physical model of a pendulum and animate it.

Tcl

Works with: Tcl version 8.5

and

Library: Tk

<lang tcl>package require Tcl 8.5 package require Tk

1. Make the graphical entities

pack [canvas .c -width 320 -height 200] -fill both -expand 1 .c create line 0 25 320 25 -width 2 -fill grey50 -tags plate .c create line 1 1 1 1 -tags rod -width 3 -fill black .c create oval 1 1 2 2 -tags bob -fill yellow -outline black .c create oval 155 20 165 30 -fill grey50 -outline {} -tags pivot

1. Set some vars

set points {} set Theta 45.0 set dTheta 0.0 set pi 3.1415926535897933 set length 150 set homeX 160

1. How to respond to a changing in size of the window

proc resized {width} {

   global homeX
   .c coords plate 0 25 $width 25
   set homeX [expr {$width / 2}]
   .c coords pivot [expr {$homeX-5}] 20 [expr {$homeX+5}] 30
   showPendulum

}

1. How to actually arrange the pendulum, mapping the model to the display

proc showPendulum {} {

   global Theta dTheta pi length homeX
   set angle [expr {$Theta * $pi/180}]
   set x [expr {$homeX + $length*sin($angle)}]
   set y [expr {25 + $length*cos($angle)}]
   .c coords rod $homeX 25 $x $y
   .c coords bob [expr {$x-15}] [expr {$y-15}] [expr {$x+15}] [expr {$y+15}]

}

1. The dynamic part of the display

proc recomputeAngle {} {

   global Theta dTheta pi length
   set scaling [expr {3000.0/$length**2}]

   # first estimate
   set firstDDTheta [expr {-sin($Theta * $pi/180)*$scaling}]
   set midDTheta [expr {$dTheta + $firstDDTheta}]
   set midTheta [expr {$Theta + ($dTheta + $midDTheta)/2}]
   # second estimate
   set midDDTheta [expr {-sin($midTheta * $pi/180)*$scaling}]
   set midDTheta [expr {$dTheta + ($firstDDTheta + $midDDTheta)/2}]
   set midTheta [expr {$Theta + ($dTheta + $midDTheta)/2}]
   # Now we do a double-estimate approach for getting the final value
   # first estimate
   set midDDTheta [expr {-sin($midTheta * $pi/180)*$scaling}]
   set lastDTheta [expr {$midDTheta + $midDDTheta}]
   set lastTheta [expr {$midTheta + ($midDTheta + $lastDTheta)/2}]
   # second estimate
   set lastDDTheta [expr {-sin($lastTheta * $pi/180)*$scaling}]
   set lastDTheta [expr {$midDTheta + ($midDDTheta + $lastDDTheta)/2}]
   set lastTheta [expr {$midTheta + ($midDTheta + $lastDTheta)/2}]
   # Now put the values back in our globals
   set dTheta $lastDTheta
   set Theta $lastTheta

}

1. Run the animation by updating the physical model then the display

proc animate {} {

   global animation

   recomputeAngle
   showPendulum

   # Reschedule
   set animation [after 15 animate]

} set animation [after 500 animate]; # Extra initial delay is visually pleasing

1. Callback to handle resizing of the canvas

bind .c <Configure> {resized %w}

1. Callback to stop the animation cleanly when the GUI goes away

bind .c <Destroy> {after cancel $animation}</lang>