Problem 4.79

A thin uniform disc of mass \(m\) and radius \(R\) suspended by an elastic thread in the horizontal plane performs torsional oscillations in a liquid. The moment of elastic forces emerging in the thread is equal to \(N=\alpha \varphi,\) where \(\alpha\) is a constant and \(\varphi\) is the angle of rotation from the equilibrium position. The resistance force acting on a unit area of the disc is equal to \(F_{1}=\eta v,\) where \(\eta\) is a constant and \(v\) is the velocity of the given element of the disc relative to the liquid. Find the frequency of small oscillation.