So I was given a problem about bungee jumping,and it's obviously important to know in advance how far the cord of unstretched length L will stretch for a given weight of person. Consider the cord to be a weak spring with constant k and the person is a point mass m. Air resistance and pendulum motion are ignored. Point x=0 would be the point where the person freely fell until the entire slack of the cord is extended to length L. After the person passes x=0, the cord is stretched x(t).
Simple enough right? Well I was having trouble:
find a model for x(t) defined only on the first interval of time 0<=t<=T for which x>=0. Solve for x(t) and then determine maximum elongation. I do know that I should use x(t)=A sin(ωt+ φ) but after than I'm stuck. Could anyone possibly help me?