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 given by:

• 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. \[\sin t+\frac{1}{2}\sin \,2t\]