Definition: "When a particle is subjected to two sine wave motion or two oscillatory motion at right angles, the particle describes lissajous figures".
A particle at the intersection of two circles is subjected to two sine wave motion A and B at 90 degree simultaneously. The particle will describe figures depending on the frequency and phase of A and B. In our case, the ratio of frequency is 1:2 and the two waves are in phase.
To draw lissajous figures : A moving point in both the circles are chosen. Here we should remember; during the time taken by the circle A to complete one rotation, circle B completes two. Hence the points are marked on the circles according to their speed. Then straight lines are drawn from the points. The meeting points of straight lines are marked as particle's positions. Finally all the particle's positions are joined in order and the path of the particle's motion appears and it is called lissajous figure. In our case, we get "8" like figure.
In the next chart, different lissajous figures that arises because of different frequency ratios and phases are shown.
In oscilloscope (CRO), lissajous figure are used to analyze wave forms in electronics laboratory.