Question

2. Calculate the slope of the line in your graph of the square of the period of the pendulum vs. length of the string .Galileo figured out the equation that describes the behavior of a pendulum. If you square both sides of the equation, you will find that the slope of the line is related to the acceleration due to gravity (g). Specifically, . Use your data to calculate g. How does it compare with the accepted value of ? Calculate the percent error and show your work.

Answer 1

The period is given by $T=2 \pi \sqrt{ \frac{l}{g} }$
Squaring this gives
$4 \pi ^{2} \frac{l}{g}$
Plotting this period as a function of length $l$ gives
$T=ml$
where the slope, m, is
$\frac{4 \pi ^{2} }{g}=4.0243$