All Problems Mechanical Oscillations
Problem 4.93
A uniform horizontal disc fixed at its centre to an elastic vertical rod performs forced torsional oscillations due to the moment of forces \(N_{z}=N_{m}\) cos wt. The oscillations obey the law \(\varphi=\) \(=\varphi_{m} \cos (\omega t-\alpha) .\) Find: (a) the work performed by friction forces acting on the disc during one oscillation period; (b) the quality factor of the given oscillator if the moment of inertia of the disc relative to the axis is equal to \(I\).
(a) \(A=-\pi \varphi_{m} N_{m} \sin \alpha\) (b) \(Q=\frac{\sqrt{\left(\cos \alpha+2 \omega^{2} I \varphi_{m} / N_{m}\right)^{2}-1}}{2 \sin \alpha}\).