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Mechanical Oscillations

Problem 4.87

The velocity amplitude of a particle is equal to half the maximum value at the frequencies \(\omega_{1}\) and \(\omega_{2}\) of external harmonic force. Find: (a) the frequency corresponding to the velocity resonance; (b) the damping coefficient \(\beta\) and the damped oscillation frequency \(\omega\) of the particle.

Reveal Answer
 4.87. (a) ω0=ω1ω2; (b) β=∣ω2−ω1∣/23,ω==ω1ω2−(ω2−ω1)2/12\begin{aligned} &\text { 4.87. (a) } \quad \omega_{0}=\sqrt{\omega_{1} \omega_{2}} ; \quad \text { (b) } \quad \beta=\left|\omega_{2}-\omega_{1}\right| / 2 \sqrt{3}, \quad \omega=\\ &=\sqrt{\omega_{1} \omega_{2}-\left(\omega_{2}-\omega_{1}\right)^{2} / 12} \end{aligned}
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