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

$\begin{array}{1 1} \sin t +\frac{1}{2} \sin 2t \\ \sin t +\frac{1}{2} \cos 2t \\ \cos t - \frac{1}{2} \sin 2t \\\sin t -\frac{1}{2} \sin 2t \end{array}$