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
  • A$\sin \,t\, + \,\frac{1}{2}\,\cos \,2t$
  • B$\cos \,t\, - \,\frac{1}{2}\,\sin \,2t$
  • C$\sin \,t\, - \,\frac{1}{2}\,\sin \,2t$
  • D$\sin \,t\, + \,\frac{1}{2}\,\sin \,2t$
JEE MAIN 2015, Diffcult
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