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.