Oscillating pen

A loop is formed of two parallel conductors connected by solenoid of inducation $L$ and a conducting pen of mass $m$ which can slide freely(without friction) over the conductors. There is a uniform homogeneous magnetic field of induction $B$ perpendicular to the plane of loop(horizontal plane). The distance of conductors is $l$ . At the moment $t=0$ the pen is imparted an initial velocity $v_0$ directed to the right. Find the law of motion $x(t)$ if the electric resistance is negligible.

$v_0=1 \textrm{ m/s}$ , $l=15 \textrm{ cm}$ , $m=1 \textrm{ g}$ , $L=4 \textrm{ mH}$ , $B=0.003 \textrm{ T}$

Give your answer as $\frac{x(367)}{10}$ in meters.