An electromagnetic system consists of two windings, one mounted on a stator and the other on a rotor. The self- and mutual inductances are given as

L11 = 1.0 H
L22 = 0.5 H
L12 = 1.414 cos θ H

where θ is the angle between the axes of the windings. The resistances of the windings are assumed to be negligible. Winding 2 is short-circuited, and the current supplied to winding 1 as a function of time is i1 = 14.14 sin ωt.

a. Derive an expression for the instantaneous torque on the rotor in terms of the angle θ.
b. Compute the time-averaged torque when 0 = 45°.
c. If the rotor is allowed to move, will it rotate continuously or will it tend to come to rest? If it comes to rest, at what angular position 0?