Two metal bars are fixed vertically and are connected on top by a capacitor of capacitance C. A sliding conductor AB can slide freely on the two bars. Length of conductor AB is L and its mass is m. It is connected to a vertical spring of force constant k. The conductor AB is released at time t = 0, from a position where the spring is relaxed. Taking initial position of the conductor as origin and downward direction as positive x axis, write the x co-ordinate of the conductor as a function of time. The entire space has a uniform horizon- tal magnetic field B. Neglect resistance and inductance of the circuit and assume that the bar AB always remains horizontal.

Answer

`x = (mg)/(k) (1- cos omegat)` where `omega = sqrt((k)/(m+B^(2)L^(2)C))`