A simple harmonic oscillator of angular frequency `2 "rad" s^(-1)` is acted upon by an external force `F = sint N`. If the oscillator is at rest in its equilibrium position at `t = 0`, its position at later times is proportional to :-

Options

A. `sin t - 1/2 sin 2t`
B. `sin t + 1/2 cos 2t`
C. `sin t + 1/2 sin 2t`
D. `cos t - 1/2 sin 2t`

Answer

A

Explanation

`F = F sin t rArr a = F/m sin t rArr v = - (F)/(m) cos t`
`x = - (F)/(m) sin t rArr X= vec(rx)_(1) + vec(rx)_(2) = A sin 2t - (F)/(m) sin t`