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

Options

A. a simple harmonic motion with a pariod `2 pi //omega`
B. a simple harmonic motion with a pariod `pi //omega`
C. a periodic but not simple harmonic motion with a pariod `2pi //omega`
D. a periodic but not simple harmonic motion with a pariod `pi //omega`

Answer

D

Explanation

`y = sin ^(2) omega t = (1- cos 2 omega t)/(2) rArr period T = (2pi)/(2omega) = (pi)/(omega)`
The given function is not satisfying the standered difference equation of `S.H.M(d^(2)y)/(dt^(2)) = - omega^(2)y` Hence it represent periodic motion but not S.H.M`