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.

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