EMI & SHM (JEE Advance)

A uniform magnetic field B is normal to the surface generated by the track of width ℓ and inclined at angle θ with the horizontal. An inductor of inductance L connects the top ends of track. A frictionless conducting rod of mass m and length ℓ is released at rest. Ignore resistance in circuit. As the rod moves, find : (i) Current in the inductor as a function of x (ii) Equilibrium position of the rod (iii) Position of the rod as a function of t