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) \[{{\omega }_{1}}={{\omega }_{0}}\] and \[{{\omega }_{2}}\ne {{\omega }_{0}}\]

B)    \[{{\omega }_{\,1}}={{\omega }_{\,0}}\] and \[{{\omega }_{\,2}}={{\omega }_{\,0}}\]

C) \[{{\omega }_{\,1}}\ne {{\omega }_{\,0}}\] and \[{{\omega }_{\,2}}={{\omega }_{\,2}}\]

D) \[{{\omega }_{\,1}}\ne {{\omega }_{\,0}}\] and \[{{\omega }_{\,2}}\ne {{\omega }_{\,0}}\]