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.

Explanation

The SHM along x and y are given by
`x=asinomegat` (i)
`y=asin(2omegat+pi//2)`
`=acos2omegat` (ii)
`=a(1-2sin^2omegat)=a(1-2*x^2/a^2)`
`y/a=1-2x^2/a^2impliesy=a-(2x^2)/(a^2)`
This is equation of parabola, hence, the resultant path followed by particle is parabola.