The function `sin^(2)(omega t)` represents:

Options

A. a periodic,but a simple harmonic motion with a pariod `2 pi //omega`
B. a simple harmonic motion with a pariod `2 pi //omega`
C. a simple harmonic motion with a pariod `pi //omega`
D. a periodic,but a simple harmonic motion with a pariod `pi //omega`

Answer

D

Explanation

Here `y = sin^(2) omegat`

`(dy)/(dt) = 2omega sin omega t cosomegat = omega sin 2 omegat`
`(d^(2)y)/(dt^(2)) = 2omega^(2) cos 2 omega t`
`for SHM (d^(2)y)/(dt^(2)) prop - y`
Hence function is not `SHM` but periodic from the `y-1` graph , time period is `t = (pi)/(omega)`