• 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.

    Correct Answer: C

    Solution :

                    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 \[{{\omega }_{2}}={{\omega }_{0}}\].

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