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)/(6)`
B. `(T)/(3)`
C. `(T)/(12)`
D. `(T)/(8)`

Answer

C

Explanation

`x = a sin (omegat + (pi)/(6))`
`v_("inst") = a omega cos (omegat + (pi)/(6))`
`(v_(max))/(2) = a omega cos (omegat + (pi)/(6))`
`(aomega)/(2) = a omega cos (omegat + (pi)/(6))`
`(pi)/(3) = omegat + (pi)/(6)`
`(pi)/(6) = (2pi)/(T)t " "rArr t = (T)/(12)`