lissajous curves/figures

Jun 2019
I have found myself in a position where i need to learn more about lissajous curves/figures. I have come across them before but only ever setup equipment to show the different types of patterns.
I now need to understand more on how to use and interpret a lissajous in a practical sense as in how to make sense of the patterns when hooked up to a circuit.
Can anyone explain how a lissajous is used and how to make sense of the images produced. Or maybe point me in a direction that may help me to learn more about them with out going too glass eyed?
Aug 2010
What have you already looked up about them? It has been a very long time since I dealt with Lissajous figures but a Google search gave several websites. This one:
defines them as "graph of a system of parametric equations x=Asin(at+δ), y=Bsin(bt)" (I hadn't remembered the "\(\displaystyle +\delta\)", I just used x= A sin(at) and y= B sin(bt) so the curves all passed through (0, 0).)
  • Like
Reactions: 1 person
Jun 2016
Alternatively try:
<Lissajous Figure Definition>

"any of a number of characteristic looped or curved figures traced out by a point undergoing two independent simple harmonic motions at right angles with frequencies in a simple ratio."

This gives a hint toward the type of usages I have seen them used for,
comparing the characteristics of two (related) signals.

If you feed a sinusoidally varying signal into the X channel of an oscilloscope
and a different sinusoidally varying signal into the Y channel of the oscilloscope
then it will display Lissajous figures.

The pattern of the figure has a direct relationship with the frequency differences of the signals
  • Like
Reactions: 1 person