The x and y displacements of a particle are x(t)=a sin ω t and y(t)=a sin 2ω t. Its trajectory will look like

Question

Accepted Answer

(3) a figure of eight lying on its side, crossing itself at the origin. The frequency ratio is 2:1, which is the simplest Lissajous figure after the conics. Using sin 2ω t=2 sin ω t cos ω t gives y=(2x)/a√a²-x², taking both signs of the root. The curve passes through the origin twice, once going up and once going down, tracing a figure of eight lying on its side.

The x and y displacements of a particle are x(t)=a sin ω t and y(t)=a sin 2ω t. Its trajectory will look like

Step-by-step solution

Why the other options are wrong