Lissajous Figures

Manipulate[ParametricPlot[{Sin[at],Sin[bt+ϕ]},{t,0,tmax},PlotRange->1.05,Axes->ax,ImageSize->{500,400},PerformanceGoal->"Quality"],
{{a,1,"horizontal frequency"},1,3,Appearance->"Labeled"},
{{b,1,"vertical frequency"},1,3,Appearance->"Labeled"},
{{ϕ,Pi/4,"relative phase"},0,2Pi,Appearance->"Labeled"},Delimiter,
{{tmax,100,"length"},0.1,500,Appearance->"Labeled"},
{{ax,False,"show axes"},{True,False}}]

CAPTION

Lissajous figures are parametric curves where both x(t) and y(t) are sine functions. If the ratio of the frequencies is rational, the curve will always eventually close. If it is irrational, the curve will never close and eventually fill a region.

DETAILS

Lissajous figures are easy to make on an oscilloscope.

THIS NOTEBOOK IS THE SOURCE CODE FROM

"Lissajous Figures" from the Wolfram Demonstrations Project
 http://demonstrations.wolfram.com/LissajousFigures/

Contributed by: Stephen Wolfram

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ParametricPlot[{Sin[t],Sin[t+π/2]},{t,0,2 π},PlotRange->1.05,Axes->True,ImageSize->{250,250},PerformanceGoal->"Quality"]

(* Geometric Mean *)
Fc = (Sqrt[20*30]);
Print["Center frequency = "<>ToString[Round[Fc,0.01]]<>" MHz"]

t=Table[{"  "<>ToString[x]<>" MHz   ",ToString[Round[((Fc-x)/Fc) 360,0.1]]<>"°  "},{x,15,30,0.5}];
Grid[t,Frame->All]