You should now have figured out that the power law for a pendulum
can be linearized using logarithms to
How can we separate from the power ?
Rearrange the equation!
From Determining the Uncertainty on the Intercept of a Fit, we know that the intercept in this case, can be determine from the average x and y values (as all fit lines must pass through this point!):
Divide through by the power (i.e. the slope of our line)
and rearrange to isolate
Thus, you can use the power , as measured by the slope, and the average values and to get . Since we assume that the average values do not have uncertainty, we can use the uncertainty on the power and a Monte Carlo error propegation to determine the uncertainty .