All Problems

Mechanical Oscillations

Problem 4.77

Find the quality factor of a mathematical pendulum \(l=\) \(=50 \mathrm{~cm}\) long if during the time interval \(\tau=5.2 \mathrm{~min}\) its total mechanical energy decreases \(\eta=4.0 \cdot 10^{4}\) times

Reveal Answer
Q=1/24gτ2lln⁡2η−1=1.3⋅102Q=1 / 2 \sqrt{\frac{4 g \tau^{2}}{l \ln ^{2} \eta}-1}=1.3 \cdot 10^{2}
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