The time period of S.H.M. is 16 seconds and it starts motion from the equililbrium position, after two seconds the velocity is `pi m//s`. Then the displacement amplitude is

Options

A. `sqrt(2) m`
B. `2 sqrt(2) m`
C. `4 sqrt(2) m`
D. `8 sqrt(2) m`

Answer

D

Explanation

`T=(2pi)/(omega) therefore omega=(2pi)/(16)=(pi)/(8)`
`v=Aomegacosomegat`
`therefore pi=A(pi)/(8)cos((pi)/(4))`
`1=(A)/(8)xx(1)/(sqrt(2))`
`therefore A=8sqrt(2)`