A particle performs `SHM` on x- axis with amplitude `A ` and time period period `T` .The time taken by the particle to travel a distance `A//5` string from rest is

Options

A. `(T)/(20)`
B. `(T)(2pi)cos^(-1)((4)/(5))`
C. `(T)/(2pi)cos^(-1)((1)/(5))`
D. `(T)/(2pi)sin^(-1)((1)/(5))`

Answer

B

Explanation

As the particle starts from rest, i.e., from extreme position `x=A sin(omega t-phi)`
At `t=0,x=Aimpliesphi=(pi)/(2)`
`A=(A)/(5)=A cos omega t`
`(4)/(5)=cos omega timpliesomega t=cos^(-1)""(4)/(5)`
`t=(T)/(2pi)cos^(-1)((4)/(5))`