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

Options

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

Answer

B

Explanation

Here, `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) prop (-y)`
Hence, function is not `SHM`, but periodic.
From the `y-t` graph, time graph period is
`t = (pi)/(omega)`.