The shortest distance travelled by a particle executing S.H.M. from mean position in 4 seconds is eual to `(1)/(sqrt(2))` times its amplitude. Find the time period.
Hint `: t=4 s , x = (1)/(sqrt(2)) , T=?`
`x = A sin omega t , omega = ( 2pi)/( T )`
Solve to get T.

Explanation

`x= A sin omega t `
`(1)/(sqrt(2))A = A sin .(2pi)/(T) xx 4`
`(1)/(sqrt(2)) A = A sin . (8pi)/(T)`
` ( 8pi)/(T) = (pi)/(4)`
`T= 32 s`