A simple harmonic oscillator of angular frequency $2\; rad\; s^{-1}$ is acted upon by an external force $F = \sin t\; N$. If the oscillator is at rest in its equilibrium position at $t=0$, its position at later times is proportional to :

Question

( A ) $\cos t - \frac{1}{2} \sin 2 t$
( B ) $\sin t + \frac{1}{2} \cos2 t$
( C ) $\sin t + \frac{1}{2} \sin 2 t$
( D ) $\sin t - \frac{1}{2} \sin 2 t$