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

Options

A. a periodic, but not simple harmonic motion with a period 2p/w
B. a periodic, but not simple harmonic motion with a period p/w
C. a simple harmonic motion with a period 2p/w
D. a simple harmonic motion with a period p/w

Answer

D

Explanation

`y = sin^(2) omega t`

`(dy)/(dt) = 2 omega sin omega t cos omega t = omega sin 2 omega t`
`(d^(2)y)/(dt^(2)) = 2 omega^(2) cos 2 omega t`
For SHM, `(d^(2)y)/(dt^(2)) alpha - y`
Hence, function is not SHM, but periodic. From the y-t graph, time period is
`t = (pi)/(omega)`