Relationship between frequency and length of pendulum

[Ace.]

Homework Statement

We calculated times of the periods of varying pendulum lengths. (20cm, 40cm, 60cm, 80cm). Then the frequency was calculated for each length and then a frequency-length graph was made. Since the graph is an exponential relationship we graphed our values on a log-log chart. Then we found the equation y = kxⁿ, where k is the value of y where x = 1, and n is the slope.

the following equation was found from the log-log chart, wehre f is the frequency and L is the length:
f = 1.5L^{-0.5}

What is the equation that relates frequency to length in a pendulum?

Homework Equations

T = 2\pi\sqrt{\frac{L}{g}}
f = 1.5L^{-0.5}

The Attempt at a Solution

I can come up with the equation for f from using the first equation

\frac{1}{f} = 2\pi\sqrt{\frac{L}{g}}
f = \frac{1}{2\pi\sqrt{\frac{L}{g}}}

But my issue is does the equation I found for my log-log chart (f = 1.5L^{-0.5}) play any role in finding the relationship? What is the significance of this equation? Would there be a way to derive f = \frac{1}{2\pi\sqrt{\frac{L}{g}}} using it?

 

[jackarms]

No, the equation you're finding is the theoretical one, and the equation you found from the data is the experimental one. They don't really have anything to do with one another, except that the theoretical one can verify the quality of the experimental one.