GraphingCalculator 4;
Window 46 6 859 1202;
PaneDivider 168;
SignificantDigits 14;
FontSizes 14;
SliderControlValue 0;
2D.Scale 0.1 0.1 5 5;
2D.BottomLeft -0.23125 0.89375;
2D.GraphPaper 0;
2Dp.BottomLeft -1 -0.453125;
2Dp.GraphPaper 0;
Text "Plots of the amplitude and phase of the steady-state response of a damped oscillator to a sinusoidal driving force as functions of driving frequency.

Version 0.3 3-31-10
";
Color 4;
Expr k=9,m=1;
Color 8;
Expr d=b/(2*m);
Color 7;
Expr a=sqrt(W_0^2-d^2);
Color 7;
Expr W_0=sqrt(k/m);
Text "A,B – amplitude; k – spring constant; m – mass, b – damping constant; d – damping parameter; a – angular frequency; W – natural frequency.  
Phase of response defined so that steady-state response is Xcos(Wt-P).";
Color 2;
MathPaneSlider 3;
Expr F_0=slider([0,5,10]);
Color 4;
MathPaneSlider 2;
Expr b=slider([0,5,40]);
Color 2;
Expr function(X,x,d)=[F_0/m]/sqrt([W_0^2-x^2]^2+4*d^2*x^2);
Color 6;
Expr X_m=F_0/m/(2*d*a);
Expr y=function(X,x,g),in(g,set(0.4,0.6,1));
Color 2;
Expr y=function(X,x,d);
Color 5;
Expr P=atan([2*d*f/(W_0^2-f^2)]);
Color 2;
Expr function(P,x)=branch(if(atan([2*d*x/(W_0^2-x^2)]),x<W_0),if(atan([2*d*x/(W_0^2-x^2)])+pi,x>W_0));
Color 2;
Expr prime(y)=function(P,prime(x));
Color 17;
Expr prime(y)=a*pi/2,in(a,set(1,2));
Color 3;
Expr R=sqrt(W_0^2-(2*d^2));
Color 17;
Expr prime(x)=W_0;
Text "Natural frequency; resonant frequency; frequency of (under)damped oscillator. ";
Color 17;
Expr x=W_0;
Color 17;
Expr x=R;
Color 17;
Expr x=sqrt(W_0^2-d^2);
Color 17;
Expr y=X_m;
Text "FWHM is about 2d for light damping:";
Color 17;
Expr R-d<x<R+d,y<function(X,x,d);
Text "Response to a constant driving force:";
Color 17;
Expr y=[F_0/m]/W_0^2;
Text "F0 – magnitude of driving force; f – frequency of driving force; X – amplitude of driven oscillation; P – phase of driven oscillation; R – resonant frequency; Xm – (approximate) amplitude at resonance";
Text "
Author: David A. Craig <<http://web.lemoyne.edu/~craigda/>";