A particle, with restoring force proportional to displacement and resulting 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 is maximum for `omega=omega_(2)`, then

Options

A. `omega_(1)=omega_(0) ` and `omega_(2)!=omega_(0)`
B. `omega_(1)=omega_(0) ` and `omega_(2)=omega_(0)`
C. `omega_(1)!=omega_(0) ` and `omega_(2)=omega_(0)`
D. `omega_(1)!=omega_(0) ` and `omega_(2)!=omega_(0)`

Answer

C

Explanation

Amplitude resonance takes place at a frequency of external force which is less than the frequency of undampled vibrations. The velocity resosnace (max. energy) takes place when frequency of external periodic force is equal to the natural frequency of undamped vibrations.