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

Options

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

Answer

A

Explanation

`y="sin"^(2) omegat=(1-"cos" 2 omega t)/(2)=(1)/(2)-("cos" 2 omega t)/(2)`
Thus it is a periodic motion but it is not a S.H.M. because it does not satisfy the equation, `(d^(2)y)/(dt^(2))=- omega^(2)y`
It angular speed `= 2 omega`
`therefore T= (2pi)/("Angular speed")=(2pi)/(2omega)=(pi)/(omega)`