A string of negligible mass, natural length L has Young's modulus Y...

A string of negligible mass, natural length $L$ has Young's modulus $Y$. The string hangs from roof with masses $m_1$ and $m_2$ as shown in the figure. If mass $m_2$ is removed gently, the mass $m_1$ is just able to bounce back upto point $O$. Find the ratio $\mathrm{m}_2 / \mathrm{m}_1$. (string will not obstruct the motion of mass $\mathrm{m}_1$ and system is initially in equilibrium).