The girl is momentarily at rest in the position shown. If the unstretched length and

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Let's assume the girl's height is h and the girl's mass is m. The girl is momentarily at rest, so the kinetic energy of the girl would be zero. The potential energy of the girl is the combination of the gravitational potential energy and elastic potential energy. 

As the string increases, the girl's elastic potential energy increases, which decreases the gravitational potential energy.

Let assume the extension in the string is \({s_1}\;{\rm{and}}\;{s_2}\), and the stiffness is \({k_1}\;{\rm{and}}\;{k_2}\).

The energy of the system always remains constant. So, the Decrease in the gravitational potential energy would equal the increase in the elastic potential energy.

\(mgh = \frac{1}{2}{k_1}s_1^2 + \frac{1}{2}{k_2}s_2^2 \)