Two linear SHM of equal amplitudes `A` and frequencies `omega` and `2omega` are impressed on a particle along `x` and `y - axes` respectively. If the initial phase difference between them is `pi//2`. Find the resultant path followed by the particle.

Answer

A, B

Explanation

`x = Asin omega t` …(i)
`y = Asin(2omega t + pi//2)`
`= Acos 2 omega t`
`= A(1 - 2 sin ^(2)omega t)`
From Eq. (i),
`sin omega t = (x)/(A)`
`:. Y = A (1 - (2x^(2))/(A))`.