Lab 22 Physical Pendulum Lab

Partners: Matthew Ibarra, Billy Justin
Date of Lab: 28 November 2016 

Lab 22 Physical Pendulum 

Mission Statement:To first derive expressions for the period of  various physical pendulums, then to verif your predicted periods by experiment. 

Theory and Experimental Procedure: For the sake of expediting the duration of the lab, most of the calculations involved had already been completed during previous exercises. We were expected to begin the lab equipped with our completed derivations for the respective center of mass and moment of inertia of a ring and triangle so that we merely need collect the dimensions of our pendulums and promptly plug them into our formulas to obtain our anticipated, theoretical values.

The derivations for the ring and the associated theoretical values are shown below, together with our collected experimental values and the associated percent error.

Above, we see that our theoretical value for the period was expected to be 1.067 seconds, and the experimental  value resulted in being  1.071 seconds, which yielded a percent error of 0.37%, well within our permissible margin of error. Below are photographs of the experiment proper.

Our apparatus consisted of a photo-gate which detected a blue tape strip as the ring oscillated back and forth. The sensor would then input the detected interruptions into LoggerPro, which in turn produced the graph shown below.

From the graph shown above, the mean value for the duration of time between two interruptions (the period) was 1.071 seconds, considerably close to our expected value.
Next we were tasked with determining the period of an isoseles triangle pivoting around an apex and base, respectively. Plugging into our derived equations and then proceeding to conduct the experiment ourselves, we obtained the following data.

For the trial during which the triangle pivoted about the apex, we obtained a theoretical value of 0.72 seconds and an experimental value of 0.72445 seconds, yielding a percent error of 0.6%, again well within the margin of error. Below are photographs documenting the apparatus setup and the graph from which we obtained our experimental value.

Above is the graph displaying the experimental value of the period for our triangular pendulum when pivoting about its apex. Below is the same triangle, except now pivoting about the midpoint of its base.

For the trial during which the triangle pivoted about the base midpoint, we obtained a theoretical value of 0.6238 seconds and an experimental value of 0.6237 seconds, identical to the thousandths place, yielding a percent error of 0.016%, our smallest ever percent error.
Conclusion: 
It should be noted that the data that I decided to include into this lab for the triangle-pivoting-about-apex pendulum is actually from our second attempt. Our first attempt yielded a percent error of 9%, which is not tolerable, and later attributed to the added weight and aerodynamic drag of the excess masking tape and a previously-thought-to-be-negligible paperclip, which we promptly removed, shown below. Upon removing these protrusions, our percent error fell from 9% to far more reasonable parameters. Even so, we knew the paperclip located at the pivot point shouldn't be contributing to this discrepancy, since there the net torque is zero. After resolving the detrimental effects of the other paperclip and excess tape, our experimental and theoretical values corresponded very well, giving credence to the physical models which we employed.