$5.(20$ points$)$ A bungee jumper with a mass of $72\mathrm{.}3$ kg ties one end of an elastic rope to a bridge and the other end to himself. The rope has a length of $\backslash ($ L$=64\mathrm{.}1\backslash$mathrm$\{$~m$\}\backslash ),$ and a stiffness per unit length of $\backslash ($ q$=5\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$m$\}^\{2\}\backslash ).$ Assuming the bridge is rigid, and that the rope has internal damping of $\backslash (50\backslash$mathrm$\{$~N$\}-\backslash$mathrm$\{$s$\}/\backslash$mathrm$\{$m$\}\backslash ),$ determine the position of the bungee jumper about his static equilibrium position for all time. Hint: Consider when the jumper is a distance $\backslash ($ L $\backslash )$ below the bridge as time $\backslash ($ t$=0\backslash$mathrm$\{$~s$\}\backslash ).$