Acceleration due to Gravity

Gravity is one of the most mysterious and important forces of the universe, so I wanted to measure exactly how much of a tug it had on my life (beware of stupid puns). A precise method to measure the gravitational acceleration constant is with a pendulum. The period of a pendulum's swing is related to the length of its string and the force of gravity. The equation is T² = 2 * pi * sqrt(L/g). If we rearrange this to solve for g, it is g = (4 * pi² * L) / T². Thus, all I had to do was build a pendulum, note the length of the string, and measure its period.

In the picture to the right you can see the basic construction of my pendulum. For the weight on the end, I eventually decided on a silver dollar that had been made into some sort of belt buckle. Thus it had a metal band on the back, perfect for attaching a piece of string. The weight was good, a little under one ounce. The empty plastic pen casing is for the fulcrum, through which the string is fixed.

Above you can see part of my pendulum. I was unable to take a picture of the entire apparatus, because it stretches over six feet. I used a CBL 2 data collection system with a photogate to have accurate timing information. The string is long in order to maximize the swept arc, and the angular momentum. The laws of pendulums state that the period of a pendulum is independent of its starting angle; this is what allows pendulum-based clocks to keep time accurately. I wanted approximately 10 degrees, so after measuring my string at 1.923 meters in length, I used trigonometry to solve for the distance horizontally from the resting point to initially hold the pendulum. This was 1.923sin 10°, or about 33 centimeters. After releasing, I let the pendulum oscillate for 45 periods. Below is a data table:

The average period was 2.7848 seconds, with a standard deviation of 0.0029 seconds. These were highly accurate results. Using the equation g = 4*L*pi^2 / T^2, I calculated the local value of g to be 9.789 m/s^2. At first glance, it appears to be about 0.02 m/s^2 below the known value of 9.80665 m/s^2. However, gravity varies slightly with latitude. Since I am in Phoenix, AZ my latitude is 33° N (see coordinate measurement). According to a table, g should be 9.79569 m/s^2 for my altitude. The difference can be explained by error, such as friction on the string rotating at the pen casing, however with the low variance in results I'm unsure of the discrepancy.