Determining a model to predict the dynamic stretch of a bungee cord

We have set about the goal of developing a bungee jump system that will provide an ideal experience for a falling egg by maximizing the passenger’s free fall time, minimizing the force it experiences during deceleration, and not allowing the passenger to hit the ground. In order to develop an ideal bungee system, we must first determine the properties of our bungee cord. Under the assumption that our cord behaves similarly to a spring, we have begun to analyze the properties of our cord in terms of Hooke’s law. According to Hooke’s law, the stretch x of an ideal spring is proportionally related to the restoring force F that acts against the pulling force of a weight attached to a hanging spring or cord. For an ideal spring, these variables are related by a spring constant k in the following equation: