question_answer

In forced oscillation of a particle, the amplitude is maximum for a frequency\[{{\omega }_{1}}\]of the force, while the energy is maximum for a frequency \[{{\omega }_{2}}\]of the force, then                            [AIEEE 2004]

A)  \[{{\omega }_{1}}={{\omega }_{2}}\]

B)  \[{{\omega }_{1}}>{{\omega }_{2}}\]

C) \[{{\omega }_{1}}<{{\omega }_{2}}\]when damping is small and\[{{\omega }_{1}}>{{\omega }_{2}}\] when damping is large

D)  \[{{\omega }_{1}}<{{\omega }_{2}}\]

Correct Answer: A

Solution :

[a]

For amplitude of oscillation and energy to be maximum, frequency of force must be equal to the initial frequency and this is only possible in case of resonance.

In resonance state,