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A graph shows the average power absorbed (P_av) by a driven oscillator plotted against the driving frequency. Consider the following statements: (1) The sharpness of the resonance peak is determined by the damping constant. (2) The sharpness of resonance is defined by the ratio (omega2 - omega1) / omega0, where omega1 and omega2 are the half-power frequencies and omega0 is the resonant frequency. (3) Maximum power is absorbed at the frequency of velocity resonance. Which statements are correct?

1. (A) (1) and (2)
2. (B) (2) and (3)
3. (C) (1) and (3)
4. (D) (1), (2) and (3)

Correct answer: (C) (1) and (3)

Solution

At velocity resonance (omega = omega0), impedance is minimum (purely resistive), so current/velocity amplitude is maximum and power absorbed is maximum. The Q-factor = omega0/(omega2 - omega1), so statement (2) has the ratio inverted and is false.

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