this can be done by the work - energy principle
1) when rope becomes taut, the potential energy stored on the point O is converted to the kinetic energy. (when the point where string become taut is considered as the datum level). so it's just E_p = E_k.
2)apply work-energy principle from point O to the point 4.4 below form the point O(take as A). Take A as the datum, so the potential energy at O is stored in the elastic string
3) you know the strain of the string so you can find the stored energy.
4)do the same thing that is done in the question 2), but in here there is an additional energy type apart from the elastic energy (ie kinetic energy). So take a point 3.2m below O as the datum and apply work-energy principle