The problem describes the technique of calculating magnetic flux, induced emf, current in a loop kept in a uniform magnetic field and undergoing some twist. It also calculates equation of motion.

A conducting loop of area A and total resistance R is suspended by a torsion spring of constant k in a uniform magnetic field
B=B e_y. The loop is in the yz plane at equilibrium and can rotate about the z -axis with the moment of inertia I as shown in figure. The loop is displaced by a small angle Theta from equilibrium and released.
Assume the torsion spring is non-conducting and neglect self-inductance of the loop.

(a) What is the equation of motion for the loop in terms of the given parameters?

(b) Sketch the motion and label all the relevant time scales for the case when R is very large.