Solving perpendicular oscillation problems- lissajous

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To solve perpendicular oscillation problems involving Lissajous figures, one must consider the variances in frequency and phase of the oscillatory systems. The solution involves treating the two oscillations as independent equations of motion, where individual trigonometric functions are calculated at various time points. These points are then plotted within a rectangular coordinate system to create the Lissajous graph. Clarification on specific passages from the MIT Introductory Physics text by A.P. French can help address any confusion. Understanding these concepts is crucial for accurately drawing and interpreting Lissajous figures in oscillation and wave studies.
SteveDB
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solving perpendicular oscillation problems-- lissajous

Hi all.
Ok, I am not getting how we're to solve perpendicular oscillatory systems.
How do the variances in frequency, and phase play into the drawing/solving of these systems?
Oh, and this is not a trig class I'm doing. It's an oscillation/wave class.
Do we solve for the individual trig functions, at various points in time, and mark our points within the rectangle, and then draw our lissajous graph?
Some serious clarification would be appreciated.
For what it's worth, I'm using the MIT Intro. Physics Series, A.P. French-- Vibrations and Waves text.
Thanks.
 
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How we're to solve them? Like we would two independant equations of motion (cuz that's what they are).

How to draw their Lissajous figure? Using the method explained thoroughly by French. If you don't understand it, tell me exactly where/what passage confuses you and I'll try to explain it better.
 
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