• # question_answer                 A particle, with restoring force proportional to displacement and resisting force proportional to velocity is subjected to a force $F\sin \omega t$. If the amplitude of the particle is maximum for $\omega ={{\omega }_{1}}$ and the energy of the particle maximum for $\omega ={{\omega }_{2}}$, then: A)                 $\omega ={{\omega }_{0}}$ and ${{\omega }_{2}}\ne {{\omega }_{0}}$                                                            B)                 ${{\omega }_{1}}={{\omega }_{0}}$ and ${{\omega }_{2}}={{\omega }_{0}}$ C)                 ${{\omega }_{1}}\ne {{\omega }_{0}}$ and ${{\omega }_{2}}={{\omega }_{0}}$                                                             D)                 ${{\omega }_{1}}\ne {{\omega }_{0}}$ and ${{\omega }_{2}}\ne {{\omega }_{0}}$                 where ${{\omega }_{0}}\to$natural angular frequency of oscillations of particle.

In driven harmonic oscillator, the energy is maximum at ${{\omega }_{2}}={{\omega }_{0}}$ and amplitude is maximum at frequency ${{\omega }_{1}}<{{\omega }_{0}}$in the presence of damping. So ${{\omega }_{1}}\ne {{\omega }_{0}}$ and ${{\omega }_{2}}={{\omega }_{0}}$.