Problem 4.81

A conductor in the shape of a square frame with side \(a\) suspended by an elastic thread is located in a uniform horizontal magnetic field with induction \(B\). In equilibrium the plane of the frame is parallel to the vector B (Fig. 4.25). Having been displaced from the equilibrium position, the frame performs small oscillations about a vertical axis passing through its centre. The moment of inertia of the frame relative to that axis is equal to \(I,\) its electric resistance is \(R\). Neglecting the inductance of the frame, find the time interval after which the amplitude of the frame's deviation angle decreases e-fold.