Problem 1.139

A smooth rubber cord of length \(l\) whose coefficient of elasticity is \(k\) is suspended by one end from the point \(O\) (Fig. 1.33). The other end is fitted with a catch \(B\). A small sleeve \(A\) of mass \(m\) starts falling from the point \(O .\) Neglecting the masses of the thread and the catch, find the maximum elongation of the cord.