A conducting rod `PQ` of mass `m` and length `l` is placed on two long parallel (smooth and conducting) rails connected to a capacitor as shown. The rod `PQ` is connected to a non conducting spring of spring constant `k`, which is initially in relaxed state. The entire arrangement is placed in a magnetic feild perpendicular to the plane of figure.
Neglect the resistance of the rails and rod.
Now, the rod is imparted a velocity `v_(0)` towards right, then acceleration of the rod as a function of its displacement `x` given by