Problem 1.191

A particle moves along a closed trajectory in a central field of force where the particle's potential energy $U=k r^{2}(k$ is a positive constant, $r$ is the distance of the particle from the centre $O$ of the field). Find the mass of the particle if its minimum distance from the point $O$ equals $r_{1}$ and its velocity at the point farthest from $O$ equals $v_{2}$