MA2051 - Ordinary Differential Equations
Project 2 - Was Hooke a Bungee Jumper - A96

Suspend a mass from a rubber band or a bungee cord. Is it reasonable to model this system using the Hooke's Law relation ? Does the usual linear spring-mass model accurately predict the period of oscillation of such a system?

Answer these questions. Conduct some experiments with a rubber band-mass system of your choice to test your conclusions.

A rubber band can not resist compression but the ideal spring modeled by Hooke's law can. Derive a model of the rubber band system that accounts for this difference. (You might find it easier to work in a coordinate system whose origin is at the unweighted position of the end of the rubber band.) Compare predicted periods with the ideal spring system and with your experimental system.

Hint If you need a function that switches from 0 to 1 when its argument goes from positive to negative, try , where sign(y) is +1 for y > 0, 0 for y = 0, and -1 for y < 0. Type help sign in MATLAB.

The final report is due Thursday, October 10.