Error in Simple Pendulum experiment

thisbmagic32

1. The problem statement, all variables and given/known data
In Physics lab we performed a simple pendulum with an apparatus that involved a cylindrical mass. We measured the period dependence on mass, amplitude, and length.
Throughout our experimentation we assumed that the mass used behaved similar to a point mass.
After analyzing our data we noticed some deviation from theory.
I am attempting to demonstrate that this deviation is due to the assumption that the mass is a point mass., and would like to determine the magnitude of the error I can attribute to this.




2. Relevant equations
For a pendulum with a point mass the net torque tau is

tau = I*alpha = F*d where I is the moment of inertia of the weight/mass

and F is the component of the gravitational force acting perpendicular to the arm length of the pendulum

3. The attempt at a solution

I am trying to show that in addition to the torquing force causing the mass to continue moving in its circular motion path, at the high point of the trajectory an additional torquing force is causing the cylindrical mass to fall (since the center of mass of the weight is no longer underneath the base there's a torquing force causing it to change its orientation).

However, I don't know how to determine what this torquing quantity is?

Can someone guide me in the right direction?

thisbmagic32

What I mean is that at the high point in the pendulum's trajectory there is a restoring torquing force causing the mass to continue moving in the pendulum trajectory AND IN ADDITION a torquing force causing the cylindrical mass to fall/sway because it's center of mass is no longer underneath its base, changing its orientation

denverdoc

was the arm of the pendulum rigid? Was there flex about the attatchment point between the mass and the arm? Was the error greater with increasing amplitude beyond what you would expect from small angle approximation?

thisbmagic32

the set-up utilized a cylindrical mass tied to a fishing cable, swinging around some vertex.
as far as I could tell the tension in the cable kept it quite rigid
however, we assumed that the mass was similar to a point mass rotating about an axis

the error with the assumption was greater than what we expect with the small angle approximation, therefore I am trying to model what the period would be if we did not assume it to be a point mass


Right now I'm treating it as a rod rotating about an external axis and attempting to calculate its period by using the parallel axis theorem

is there any other/better way to treat this?

thisbmagic32

yes, that is why the mass is able to sway on the arm

denverdoc

see if this is of any help:

http://farside.ph.utexas.edu/teachin...s/node141.html