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Question

During the phenomenon of resonance:
  1. The amplitude of oscillations becomes large
  2. The frequency of oscillations becomes large
  3. The time period of oscillation becomes large
  4. All of the above 


Solution

The correct option is A The amplitude of oscillations becomes large
Angular frequency of free damped oscillations is given by
ω=ω20γ2
When γ<<ω0 (i.e weak damping), then ωω0.
The maximum amplitude of forced oscillations is given by
Amax=F02mγ(ω20γ2) .....(1)
At resonance, Amax=F02mγω0.

Clearly this is the largest value , as for ω<ω0 or ω>ω0, the denominator value of (1) increases, thus the value of Amax decreases.
Thus, during the phenomenon of resonance, the amplitude of oscillation becomes large, because applied frequency is equal to natural frequency.

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