The displacement of a particle is represented by the equation `y = sin^(2) omega t` the motion is

Options

A. non - periodic
B. periodic but not simple harmonic
C. simple harmonic with period `2 pi // omega`
D. simple harmonic with period ` pi // omega`

Answer

B

Explanation

Given equation of motion is
`y = sin^(3) omega t`
`= (3 sin omega t - 4 sin 3 omega t)//4`
`[:' sin 3 theta = 3 sin theta - 4 sin^(3) theta]`
`rArr (dy)/(dt) = [(d)/(dt) ( 3 sin omega t) - (d)/(dt) (4 sin 3omega t)]4`
`rArr 4(dy)/(dt) = 3 omega cos t - 4 xx [3 omega cos 3 omega t]`
`rArr 4 xx (d^(2)y)/(dt^(2)) = - 3 omega^(2) sin omega t+12 omega sin 3 omega t`
`rArr (d^(2)y)/(dt^(2)) = - (3 omega^(2) sin omega t+12 omega^(2) sin 3 omega t)/(4)`
`rArr (d^(2)y)/(dt^(2))` is not proportional to `y`
Hence motion is not `SHM`