A particle moves on the X-axis according to the equation `x=x_0 sin^2omegat`. The motion simple harmonic

Options

A. with amplitude `(x_(0)//2)`
B. with amplitude `2x_(0)`
C. with time period `(2pi//omega)`
D. with time period `(pi//omega)`

Answer

A, D

Explanation

`x = x_(0) sin^(2) omega t = (x_(0))/(2) (1 - cos 2 omega t) = (x_(0))/(2) - (x_(0))/(2) cos 2 omega t`
Frequency `omega. = 2 omega`
`rArr 2pi//T.= 2 omega`
`rArr T. = (pi//omega)`
Amplitude `= (x_(0))/(2)`