All Problems

Mechanical Oscillations

Problem 4.92

An external harmonic force \(F\) whose frequency can be varied, with amplitude maintained constant, acts in a vertical direction on a ball suspended by a weightless spring. The damping coefficient is \(\eta\) times less than the natural oscillation frequency \(\omega_{0}\) of the ball. How much, in per cent, does the mean power \(\langle P\rangle\) developed by the force \(F\) at the frequency of displacement resonance differ from the maximum mean power \(\langle P\rangle_{\max }\) ? Averaging is performed over one oscillation period.

Reveal Answer
⟨P⟩max⁡−⟨P⟩⟨P⟩max⁡=100η2−1%\frac{\langle P\rangle_{\max }-\langle P\rangle}{\langle P\rangle_{\max }}=\frac{100}{\eta^{2}-1} \%
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