A particle executing SHM with time period T and amplitude A. The mean velocity of the particle averaged over quarter oscillation, is

Options

A. `(A)/(4T)`
B. `(2A)/(T)`
C. `(3A)/(T)`
D. `(4A)/(T)`

Answer

D

Explanation

Let the displacement off the particle executing SHM at any instant t is, `x=Asinomegat`
Velocity, `v=(dx)/(dt)=(d)/(dt)Asinomegat=Aomegacosomegat`
The mean velocity of the particle averaged over quarter oscillation is
`ltvgt_(0toT//4)=(int_(0)^(T//4)vdt)/(int_(0)^(T//4)dt)=(int_(0)^(T//4)Aomegacosomegatdt)/(T//4)`
`((Aomega)/(omega)[sinomegat]_(0)^(T//4))/(T//4)=(A[sinomegat]_(0)^(T//4))/(T//4)=(4A)/(T)`