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A point performs simple harmonic oscilla...

A point performs simple harmonic oscillation of period T and the equation of motion is given by `x = a sin (omega t + (pi)/(6))`. After the elapse of what fraction of the time period, the velocity of the point will be equal to half of its maximum velocity ?

A

`T//3`

B

`T//12`

C

`T//8`

D

`T//6`

Text Solution

Verified by Experts

The correct Answer is:
B
`x=asin(omegat+(pi)/(6))`
`v=(dx)/(dt)aomegacos(omegat+(pi)/(6))`
`v_(max)=aomega`
Now, `(a omega)/(2)=a omega cos (omegat+pi//6)`
`implies omegat+(pi)/(6)=(pi)/(3)`
`implies (2pi)/(T)t=(pi)/(6)implies t=(T)/(12)`.
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