From our solution:

The system will oscillate until in comes to rest at the steady state value of A₁. Assuming no catastrophic failure of the bungee cord or the absence of gravity, this system will be stable.

The plot of the system will look like the graph below. Time is on the x-axis and distance is on the y-axis. The plot will start at the height of the jump and oscillate until the steady state height of A₁ is reached. If the calculations are correct, the oscillations will not go below ground level (or even come close to it for that matter) and the jumper will have a safe and exciting jump and will want to come back for more.