A conducting frame abcd is kept in a vertical plane. A conducting rod of of mass m and length `l` can slide smoothly on it remaining always horizontal. The resistance of the loop is negligible and inductance is constant having value `L`. The rod is left from rest and allowed to fall under gravity and inductor has no initial current. A magnetic field of constant magnitude Bis present throughout the loop pointing inwards. Determine

(a) position of the rod as a function of time assuming initial position of the rod to be `x=0` and vertically downward as the positive x-axis.
(b) the maximum current in the circuit.
(c) maximum velocity of the rod

Answer

(a) `x=(g)/(omega^(2))[1-cosomegat]`,(b) `I_("max")=(2mg)/(Bl)`, ( c) `V_("max")=(g)/(omega)`