A particle performs SHM with a period `T` and amplitude a. The mean velocity of particle over the time interval during which it travels `a//2` from the extreme position is

Options

A. `(a)/(T)`
B. `(2A)/(T)`
C. `(3A)/(T)`
D. `(A)/(2T)`

Answer

C

Explanation

`x=acosomegat`
`(a)/(2)=acosomegat_0`
or `cos(pi)/(3)=omegat_0`
or `(pi)/(3)=omegat_0` `because` `t_0=(pi)/(3omega)`
`v=(dx)/(dt)=-aomegasinomegat` `because` `overlinev=(int_0^((pi)/(3omega))vdt)/(int_0^((pi)/(3omega))dt)`
But `omega=(2pi)/(T)` `because` `overlinev=(3a)/(T)`