Daniel Guzman. Lab partners( James Okamura abd Rodrigo Uribe) Physical Pendulum.

Daniel Guzman
Physical Pendulum
Physics 4A


The purpose of this experiment was to determine the period oscillations of two different geometries, one being a semicircle and the other being a isosceles triangle, to then verify using theory.

The main theoretical idea behind this particular lab is the idea of simple harmonic motion which is a very useful idea to describe oscillation motion for any object or body, in this case we used the ideas behind simple harmonic motion to find the period of oscillation for two different shapes, to do this we first had to derive an expression to find the center of mass of the shapes and after finding it we found the moment of inertia of the shapes about the point or axis that the shapes would be rotating from. Once this is done we used the equation for toque and the relationship that exists between alpha and omega to find the angular frequency, once this angular frequency is found one can use the relationship that exists between angular frequency and period to find the period of oscillation for the geometry.

The apparatus for this experiment consisted of a photo gate, a laptop, a semicircle and an isosceles triangle. The photo gate in this experiment was used to measure the period of oscillations of the two different geometries, the laptop was used to analyze and obtain the data for the period of oscillations for the two different geometries.

The experimental procedure for this lab was quite simple due that we only had to measure the period of oscillations of two geometries. The first thing that we did was to put the bodies on a clip that went through the point from which the bodies were going to oscillate after putting the clip on the geometries we made sure that the photo gate was able to record the period of oscillations of the bodies, once this was confirmed we displaced the bodies very little and then made the measurements of the period of the two bodies once this was done, the experiment is pretty much done and the only thing to do is to compare the theoretical results to the experimental ones.

Period of oscillation for the two different bodies

Period of oscillation for the semicircle

Period of oscillation for the triangle

 

Derivations for the center of mass and moment of inertia for the two geometries

Derivation for the moment of inertia of the semicircle and its center of mass

derivation for the moment of inertia of the triangle about its apex

Derivation for the center of mass the triangle

Theoretical calculations for the period of oscillation for the two geometries

Comparing the theoretical results to the experimental results (percent error)

Conclusion: the experimental results and the theoretical results were very close to each other, which means that the experiment was carried out correctly, the percent errors as shown were very small, which lets one infer that the theoretical calculations as well as the experimental procedure was done correctly. The error in this experiment was very small, which means that the error did not affect the experimental results.