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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

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`

Text Solution

Verified by Experts

The correct Answer is:
C
`x=asin^(2)omegat`
`=a((1-cos2omegat)/(2))(because cos2theta=1-2sin^(2)theta)`
`=(a)/(2)-(acos2omegat)/(2)`
`therefore` Velocity, `v=(dx)/(dt)=(2omegaasin2omegat)/(2)=omegaasin2omegat`
Acceleration, `a=(dv)/(dt)=2omega^(2)acos2omegat`
for the given displacement `x=asin^(2)omegat,a prop-x` is not satisfied.
Hence, the motion of the particle is non simple harmonic motion.
Note : The given motion is periodic motion with a time period `T=(2pi)/(2omega)=(pi)/(omega)`
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