Question

Superposition of two oscillations give Lissajous figure. State the conditions on the oscillations and nature of superposition.

Answer 1

When the two individual rectangular vibrations are of slightly different frequencies, the resulting motion is more complex.

The relative phase is equal to

$$φ=(ω_2-ω_1)t+φ_0 (1)$$

According to formula (1), the relative phase gradually changes with time. This makes the shape of the figure to undergo a slow change. When the two vibrations are in the same phase, i.e. φ = 0, the Lissajous figure reduces to a straight line. If the amplitudes of vibrations are a, and a2, respectively, then the resulting figure always lies in a rectangle of sides 2a1 and 2a2. The patterns which are traced out are called Lissajous figures.