The time taken by a particle performing SHM to pass from point `A` to `B` where its velocities are same is `2 s`. After another `2 s` it returns to `B`. The ratio of distance `OB` to its a amplitude (where `O` is the mean position) is

Options

A. `1: sqrt(2)`
B. `(sqrt(2) - 1):1`
C. `1 : 2`
D. `1 :2 sqrt(2)`

Answer

A

Explanation

`V_(1) = V_(2)`

`t_(AB) = 2s`
`:. t_(OB) = 1s`
`t_(BCB) = 2 s`
`:. BC = 1 s`
`:. t_(OB) = t_(BC)`
`:. OB = (A)/sqrt (2)`
or `(OB)/(A) = (1)/sqrt(2)`.