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A driven damped oscillator will, after all transient motion has died out, oscillate at (A) the driving frequency. (B) the frequency of the damped but free oscillator. (C) the frequency of the undamped but free oscillator. (D) any of the above, because the frequencies are all the same.
The correct option is (A).When the damping is small, the forced oscillations reach their maximum displacement amplitude when the driving frequency is equal to the natural frequency. This condition is known as resonance and the corresponding frequency wʹʹ is called the resonant angular frequency. Thus a driven damped oscillator will, after all transient motion has died out, oscillate at the driving frequency. Therefore option (A) is correct.
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