GraphingCalculator 3.5;
Window 46 6 807 1080;
PaneDivider 231;
FontSizes 18 14 10;
2D.BottomLeft -3.296875 -4.125;
2Dp.BottomLeft -3.296875 -4.4375;
Text "Pendulum potential energy and phase space trajectories – exact and lowest order approximation.";
Color 3;
Expr m=1,g=1;
Color 4;
Expr L=1;
Color 2;
MathPaneSlider 12;
Expr E=slider([0,5,40]);
Text "m – mass; g – gravity; L – length of pendulum; E – total energy;";
Color 3;
Expr y=m*g*L/2*x^2;
Expr y=[m*g*L]*[1-cos(x)];
Color 2;
Expr y=E;
Text "First curve is the simple harmonic approximation; second is the exact expression for the energy; last is the total energy
";
Color 17;
Expr prime(y)=[m*g*L]*[1-cos(prime(x))];
Color 17;
Expr prime(y)=E;
Color 3;
Expr 1=m*L^2/(2*E)*prime(y)^2+m*g*L/(2*E)*prime(x)^2;
Expr 1=m*L^2/(2*E)*prime(y)^2+m*g*L/E*[1-cos(prime(x))];
Text "Phase curves are those of constant energy; first is the simple harmonic approximation; second is the exact energy for a pendulum.


<size=14>Author: David A. Craig <<http://web.lemoyne.edu/~craigda/>";