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Mechanical Oscillations

Problem 4.70

A point performs damped oscillations with frequency ω\omega =25 s−1.=25 \mathrm{~s}^{-1} . Find the damping coefficient β\beta if at the initial moment the velocity of the point is equal to zero and its displacement from the equilibrium position is η=1.020\eta=1.020 times less than the amplitude at that moment.

Reveal Answer
β=ωη2−1=5 s−1\beta=\omega \sqrt{\eta^{2}-1}=5 \mathrm{~s}^{-1}
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