Originally Posted by **physicsquest** Rachel, your approach seems in general to be correct (the writing is hard to follow; maybe you should have keyed it in).
However you can solve it in a simpler fashion by not bringing in K.E.
Initially the system has only grav P.E. and finally at full stretch just at ground level, it is again only elastic P.E.
Apply conservation of energy.
If L is the unstretched length of the string, we have
m g 40 = 0.5 k (40 - L)^2
Solving, we get L = 16.
I am sure r.samanta will agree with this method! |

I think that method is incorrect (or not)

and this is diferent than:

and you have to consider the beggining of SHM which is not at the begining of the jump

I am sorry if I am incorrect