A point simple harmonic oscilation of the period and the equation of motion is given by `x a sin (omega t + pi //6)` after the step of friction of the time period the velocity of the part 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)`
`v=(dx)/(dt)=aomegacos(omegat+pi//6)`
`(v_(max))/(2)=(aomega)/(2)=aomegacos(omegat+pi//6)`
`cos((2pi)/(T)t+pi/6)=1/2=cospi/3`
`(2pi)/(T)t+pi/6=pi/3implies(2pi)/(T)=pi/6`
`t=(T)/(12)`