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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