Modeling a bungee jump is very similar to modeling a vertical spring, however, in a bungee jump we must contend with air friction. To keep this model from getting too complicated, we make the simplifying assumption that the bungee cord is weightless.
The terms that feed into change in velocity are the ones typical of fall and spring models: mass, acceleration due to gravity, weight, total force, and acceleration.
The term for total force however, contains not only the restoring spring force and the weight, but also air friction, which is a function of projected area (controlled by a slider), velocity, the absolute value of velocity, multiplied by the constant for air resistance (-0.65).
Because a spring is rigid, when the weight is above the equilibrium point, the spring exerts a restoring force in the opposite direction. When a bungee cord is above the unweighted length, it is slack and exerts no opposing force, therefore, restoring spring force is conditional. To demonstrate this in Nova, the term for restoring spring force contains the following logic: (length > unweighted length) ? -spring constant * (length - unweighted length) : 0.
The graph shows the length and velocity of the bungee cord and the jumper over time.