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 ?

Options

A. T/3
B. T/12
C. T/8
D. T/6

Answer

B

Explanation

`x=asin(omegat+(pi)/(6))`
`upsilon=(dx)/(dt)=a omegacos (omegat+(pi)/(6))`
`upsilon_("max")=aomega`
`(aomega)/(2)=a omegacos(omegat+(pi)/(6))`
`omegat+(pi)/(6)=(pi)/(3)rArr omegat=(pi)/(6)`
`t=(pi)/(6omega)=(pixxT)/(6xx2pi)=(T)/(12)`