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Lissajous figures are produced by superposition of 2 SHM's in mutually perpendicular directions. For the Lissajous figure shown here, the If both SHM have same frequency, the lissajous frequency in vertical direction is times figure is simple. It may be a circle, ellipse or a the frequency in horizontal direction straight line depending on the phase difference between two SHMs. Interesting case occurs when one of the SIIM is at double frequency of another. Suppose a body executes SHM vertically with
(1) 3
(2) \( \frac{1}{3} \)
(3) 2
(4) \( \frac{1}{2} \) \( 2 \mathrm{f}_{0} \) and is initially at \( \mathrm{A} \), mean position of vertical as well as horizontal SHM. It can be seen to trace out a figure of 8 in space as shown. Since horizontal SHM has half the time period, it executes two horizontal oscillations by the time it completes a vertical oscillation.
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