x a n d y displacements of a particle are given as x t = a sin ⁡ ω t a n d y t = a sin ⁡ 2 ω t . Its trajectory will look like:

Step-by-step solution

∵       x = A sin ⁡ ω t       ⇒       s i n   ω t = x A Also, c o s   ω t =   1 - sin 2 ⁡ ω t =   1 - x 2 A 2   ⇒     cos ⁡   ω t =   A 2 - x 2 A As, y = 2 A sin ⁡ ω t cos ⁡ ω t ⇒       y = 2   A x A   A 2 - x 2 A ⇒       y = 2 A       x   A 2 - x 2   ⇒   &#1