Model Pendulum w/ Damping: Newton's Laws & Rubber Band

[bsmith6661]

I feel like this is a dumb question, but here goes: I'm trying to model a pendulum with damping. The pendulum is connected to a rubber band (unstretched when the pendulum is vertical) on the right side, and the rubber band is fixed at the other end. How would I go about modeling a rubber band using Newton's Laws? Everything needs to be in terms of m, k, and c. I know that a rubber band acts similarly to a spring, but can it be modeled as such?

 

[Dr.D]

For very small displacements, the rubber band will act approximately like a spring. For larger displacements, you will find that the rubber band is nonlinear. From you description of the system, it sounds like the rubber band will only be taut for displacements to the left. You will need to take that into account when you write the equation of motion. Gravity, of course, will act no matter which direction the pendulum is displaced.