Motion of a simple pendulum

Measure properties of a simple pendulum and perform some graphical analysis.

1. Set things up so that a 50-gram mass hangs from a long piece of string. Run the string through one of the holes in the 3-knob bar, and wrap one or two loops around a knob to hold it in place. Make sure that you can swing the mass freely when the string is 110 cm long.
2. Make measurements with at least 4 different lengths L:
   • one between 7 and 12 cm
   • one between 20 and 25 cm
   • one between 40 and 50 cm
   • one between 95 and 110 cm
   Measure L from the top of the string to the middle of mass. Measure the time to swing back-and-forth 10 times with small angular amplitude: start at an angle of about 10 degrees from the vertical. Make 2 trials at each length.
3. Make a neat table with your results, showing the average period, and uncertainty in period, in each case.
4. Add two columns to your table: square of the average period, and uncertainty in square of average period, in each case.
5. Create graph A: period vs. length. Is this a straight line?
6. Create graph B: period-squared vs. length. Is this a straight line?
7. Determine the slope of line connecting your measurements in graph B and the uncertainty in the slope.