Problem 3.387

Uniform electric and magnetic fields with strength $E$ and induction $B$ respectively are directed along the $y$ axis (Fig. 3.101). A particle with specific charge $q / m$ leaves the origin $O$ in the direction of the $x$ axis with an initial non-relativistic velocity $v_{0} .$ Find: (a) the coordinate $y_{n}$ of the particle when it crosses the $y$ axis for the $n$ th time; (b) the angle $\alpha$ between the particle's velocity vector and the $y$ axis at that moment.