A mass hangs at the end of a length L of string making a pendulum. The time it takes the pendulum to complete a swing (the period T, our y variable, measured in seconds) is recorded for various pendulum lengths (x, measured in m). The accuracy of the period measurement is 0.04 s. According to Newton's laws:

T = 2 π (L/g)^1/2

where g = 9.8 m/s² is the acceleration of gravity.

If we compare this expression to the generic power law relationship we find:

B = 1/2

A = 2 π/g^1/2

or

g = (2 π/A)²

1. Fit this data to a power law relationship.
2. Consider Newton's scientific claim of a power law. Does this evidence (data) confirm or contradict this claim? Support your answer quantitatively.
3. Properly report (sigfigs, error, units) the exponent for the best-fit power law.
4. Do an additional fit with the exponent held fixed at 0.5.
5. Properly report (sigfigs, error, units) the A parameter for this second fit.
6. Use a spreadsheet to calculate the acceleration of gravity from A, and properly report (sigfigs, error, units) the value.
7. Self-document the spreadsheet and turn in a hardcopy of the page.
8. Make a hardcopy plot of the data with best-fit curve. Make an additional hardcopy plot with scales chosen so as to linearize the curve.
9. Turn in fit reports from both fits (i.e., steps 3 and 4).