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Comparison of Data with Theoretical Expectations
The spring-only system exhibited oscillation with no apparent damping. Of course, there was some damping involved as energy was lost in the system due to friction, but in this case it is negligible. In fact, the data is best represented by a cosine function, which would be a solution to a Case 1 equation with the right initial conditions.
The mass, spring, rubber band system displayed behavior that was closest to solutions of the case 4 equations. Somehow, damping was introduced into the system when the rubber band was added that was not present before in the mass-spring system. Our conjecture as to this change in the behavior of the system is that heat leaves the rubber band as the system oscillates. The properties of rubber as a material cause it to dissipate energy. How this actually occurs and incorporating it into a differential equation would be interesting and hopefully can be the focus of future inquiry.
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