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 \(v_{2}\)