Determination of Pendulum Parameters zeta, omegan, and omegad

Remove the pendulum assebly from the cart and turn it upside down, allowing the pendulum to hang freely. Start the pendulum swinging and record the position  theta on a chart recorder. From our previous analysis we expect the response to be something like:


The response will be damped sinusoidal oscillations with a frequency omegd2p and a damping envelope of dampenvl

From your chart recording estimate the parameters  zeta, omegan,and omegad

When I performed this experiment I found the decay appeared to be linear rather than exponential. It appeared the pendulum lost a fixed amount of energy every swing regardless of how wide the swing was.


My guess is at the end of each swing when the pendulum momentarily stops the friction changes from kinetic (moving) friction to static (non-moving) friction, and it takes a certain amount of energy to overcome this static friction. zeta was estimated to be insignificantly small (0.02 as I recall, and I think we set zeta to zero to simplify the equations later on and ignored the static friction energy loss problem).