A coil of self inductance $L$ is connected at one end of two rails as shown in figure. A connector of length $l$, mass $m$ can slide freely over the two parallel rails. The entire set up is placed in a magnetic field of induction $B$ going into the page. At an instant $t=0$ an initial velocity $v_0$ is imparted to it and as a result of that it starts moving along $x$-axis. The displacement of the connector is represented by the figure.