question_answer

A particle of mass \[m\] is attached to a spring (of spring constant\[k\]) and has a natural angular frequency\[{{\omega }_{0}}\]. An external force \[F(t)\] proportional to \[\cos \,\omega t\,(\omega \ne {{\omega }_{0}})\] is applied to the oscillator. The time displacement of the oscillator will be proportional to

A) \[\frac{m}{{{\omega }^{2}}_{0}-{{\omega }^{2}}}\] 

B) \[\frac{1}{m({{\omega }^{2}}_{0}-{{\omega }^{2}})}\]

C) \[\frac{1}{m({{\omega }^{2}}_{0}+{{\omega }^{2}})}\]       

D) \[\frac{m}{{{\omega }^{2}}_{0}+{{\omega }^{2}}}\]