question_answer

A simple harmonic oscillator of angular frequency \[2rad\,{{s}^{-1}}\]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: [JEE ONLINE 10-04-2015]

A) \[\sin t+\frac{1}{2}\cos 2t\]

B)      \[\sin t-\frac{1}{2}\sin 2t\]

C) \[\cot t-\frac{1}{2}\sin 2t\]

D)      \[\sin t+\frac{1}{2}\sin 2t\]

Correct Answer: B

Solution :

[b]

at t = 0             x & velocity both has to be zero