Question

What is the applications of lissajous pattern

Answer 1

Lissajous figures can be used to graphically illustrate the relationship between two waveforms.
One waveform is entered along the X axis the other along the Y axis.
Consider trying to tune two sine wave generators to give the same frequency.
Feeding the signals into the X and Y drivers of an oscilloscope will produce a Lissajous figure.
When the display shows a stationary ellipse the two are in tune.
the ratio of one axis of the ellipse to the other indicates the relative amplitude of the two signals (which is louder).
The angle of the ellipse indicates the phase difference (Are both waves reaching the peak together or is one still in the trough when the other is at the peak).
Other (more complex) stationary figures will result from harmonic frequency differences (one frequency is an exact multiple of the other).