Determination of Pendulum Parameters
,
, and
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
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
and a damping envelope of
From your chart recording estimate the parameters
,
,and
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.
was estimated to
be insignificantly small (0.02 as I recall, and I think we set
to zero to simplify the equations later on and ignored the static friction energy loss
problem).
