A) \[{{\omega }_{1}}={{\omega }_{2}}\,and\,{{\omega }_{2}}\ne {{\omega }_{0}}\]
B) \[{{\omega }_{1}}={{\omega }_{0}}\,and\,{{\omega }_{2}}={{\omega }_{0}}\]
C) \[{{\omega }_{1}}\ne {{\omega }_{0}}\,and\,{{\omega }_{2}}={{\omega }_{0}}\]
D) \[{{\omega }_{1}}\ne {{\omega }_{0}}\,and\,{{\omega }_{2}}\ne {{\omega }_{0}}\]
Correct Answer: C
Solution :
[c] At maximum energy of the particle, velocity resonance takes place, which occurs when frequency of external periodic force is equal to natural frequency of undamped natural vibrations, i.e. \[{{\omega }_{2}}\ne {{\omega }_{0}}\]. Further amplitude resonance takes place at a frequency of external force which is less than the frequency of undamped natural vibrations, i.e. \[{{\omega }_{1}}\ne {{\omega }_{0}}\].
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