The displacement of particle along the X-axis is given by `x= a sin^(2) omega t`. The motion of the particle corresponds to………..

Options

A. Simple harmonic motion of frequency `(omega)/(pi)`
B. Simple harmonic motion of frequency `(3omega)/(2pi)`
C. Non-simple harmonic motion.
D. Simple harmonic motion of frequency `(omega)/(2pi)`

Answer

A

Explanation

Displacement of particle
`x= a sin^(2) omega t= (a)/(2) (1- cos 2 omega t)`
velocity `=(dx)/(dt)= (a)/(2) (2 omega sin 2omega t)`
and acceleration `(d^(2)x)/(dt^(2))= 2 omega^(2)a*cos (2omega t)`
From this equation `omega.= 2omega = 2pi f`
Frequency `f= (omega)/(pi)`.