GraphingCalculator 4;
Window 45 218 865 1037;
PaneDivider 380;
FontSizes 14;
BackgroundType 0;
BackgroundColor 255 255 255;
StackPanes 1;
Slider 0 50;
SliderSteps 500;
SliderControlValue 0;
T 0 100;
2D.Scale 0.25 0.5 1 2;
2D.BottomLeft -1.03125 -3.203125;
2D.Axes 0;
2D.GraphPaper 0;
Text "Simulation of a pendulum wave machine and illustration of apparent periodicity via aliasing of underlying wave

Machine consists in row of N evenly-spaced pendula of successively shorter lengths

Version 0.2";
Color 2;
Expr function(X,s,W,p,Y,A)=A*vector(sin([W*s+p]),Y);
Text "• T is overall period of pendulum wave dance
• N is total number of pendula
• d is physical separation of adjacent pendula
• M is the number of oscillations the longest (slowest) pendulum makes in time T

Pendulum m is located at physical position y_m = m*d

The key is that each successively shorter (faster) pendulum undergoes one more oscillation in time T than its immediate predecessor.";
Expr A=1,d=1;
Color 5;
Expr T=50,N=20,M=10;
Text "(Angular) frequency W of pendulum at physical position s";
Color 6;
Expr f_0=(M-1)/T,g_0=2*pi/T;
Color 4;
Expr function(W,s)=2*pi*f_0+s*(g_0/d);
Color 3;
Expr function(X,n,function(W,m*d),0,m*d,A),in(m,set(1*ldots*N));
Color 17;
Grain 1;
Expr function(X,n,function(W,t*d),0,t,A);
Text "




References:

1. J. Flaten & K. Parendo, AJP 69,778-782 (2001) 
2. P. Liu 
<< http://hippomath.blogspot.com/2011/06/pendulum-waves-mathematical-description.html>
<< http://hippomath.blogspot.com/2011/06/pendulum-waves-mathematical-description_21.html>
<< http://hippomath.blogspot.com/2011/06/pendulum-waves-mathematical-description_6472.html>
<< http://hippomath.blogspot.com/2011/06/making-your-own-pendulum-wave-machine.html>

Author: David A. Craig <<http://web.lemoyne.edu/~craigda/>

";