Lissajous figures - Ted Pavlic

Lissajous figures Lab 1: Introduction to InstrumentationECE 209:Circuits and Electronics LaboratoryALissajous ( LEE-suh-zhoo ) figureis aparametric plotof theharmonic system(x(t) =Axsin( xt+ ),y(t) =Aysin( yt+ + )( ,y(x) =Aysin y x arcsin(xAx) + where|x| Ax). ytIn our case, we plot an inputx(t) and outputy(t) of alinear time-invariant (LTI) system. Becausecomplexexponentialsareeigenfuncti onsof LTI systems and sinusoids aresums of complex exponentials, the outputfrequency will match the input frequency ( , x= y= = 2 f). Our LTI system ( , the phase-shiftercircuit) is anall-pass filter, and so it ensures thatAy=Ax=A. So we are consider the simpler system(x(t) =Asin(2 f t+ ),y(t) =Asin(2 f t+ + )( ,y(x) =Asin arcsin(xA) |{z}x ygraph has no dependence on.)))

Title: Lissajous figures Author: Ted Pavlic Subject: ECE 209 (Lab 1: Introduction to Instrumentation) Keywords: oscilloscopes, curves, parametric plots, harmonograph, Bowditch curve, harmonic motion, quadrature, engineering, linear time-invariant systems theory, LTI, eigenfunction

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