12/2/2014 SHM

Purpose:

The purpose of this experiment is to calculate the period of half circle piece of cardboard.

Experiment:

The first part of our experiment is cut out a half circle from cardboard to use for our simple harmonic motion.

Once we cut out the half circle we had to calculate the inertia from the the top and bottom of the half circle.

We used to calculus to solve inertia from the center of mass and then made the proper shifts to find the inertia from pivot of top and bottom.

Here is our calculation for inertia from center of mass.

We then created a formula to calculate the period of the using SHM.

The mas of our half circle is 0.0058kg with a radius of 0.1075.

Once we had both formulas we then predicted the period of SHM from the top as 0.714 seconds and from the bottom as of 0.613 seconds.

Here is a picture of our calculation.

 Here is a picture of are system we used a motion sensor to measure the periods which we found for the bottom 0.764s and from the top 0.694s

For the period from the pivot on the bottom we where off by 6% and for the period with the pivot on the top we where off by 11%.