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The displacement of a particle along the...

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

A

non-simple harmonic motion

B

simple harmonic motion of frequency `omega//2x`

C

simple harmonic motion of frequency `omega//2x`

D

simple harmonic motion of frquency `3omega//2pi`

Text Solution

Verified by Experts

The correct Answer is:
C
`x = a sin^(2)omegat`
` = a ((1-cos 2 omegat))/(2) rArr x = (a)/(2) - (a)/(2) cos 2 omegat `
` rArr x - (a)/(2) = - (a)/(2)cos 2 omegat`
We can see that is S.H.M. with angular frequency `2omega`.
Hence time period
`T = (2pi)/(2omega) = (pi)/(omega)`
` v = (1)/(T) = (omega)/(pi)`
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