A small mass executes linear `SHM` about `O` with amplitude a and period `T`. Its displacement from `O` at time `T//8` after passing through `O` is:

Options

A. `a//8`
B. `(a)/(2sqrt(2))`
C. `a//2`
D. `(a)/(sqrt(2))`

Answer

D

Explanation

`x = a sin omegat = a sin ((2it)/(T))`
At `t = (T)/(8), x = a sin ((2pi((T)/(8)))/(T)) = a sin (pi/4) = a/(sqrt(2))`
OR

`omega = omegat, phi = (2pi)/(T) (T)/(8) = (pi)/(4) rArr theta = (pi)/(4)`
As `costheta = (x)/(a)` so `x = (a)/(sqrt(2))`