All Problems

Mechanical Oscillations

Problem 4.92

An external harmonic force FF 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 η\eta times less than the natural oscillation frequency ω0\omega_{0} of the ball. How much, in per cent, does the mean power ⟨P⟩\langle P\rangle developed by the force FF at the frequency of displacement resonance differ from the maximum mean power ⟨P⟩max⁡\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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