Relationship between Period of a pendulum and length

1. Nov 3, 2008

Dynamite

1. The problem statement, all variables and given/known data

The formula to find the period of a pendulum is t=2pi √ L/g
where pi = 3.14....
L=length of pendulum
g=gravity

So I was wondering how all of this was put together. How they related together? Why it is multiplied by 2pi

3. The attempt at a solution
I really don't know, it's I'm asking here. I tried graphing it and it gives me a curve.

2. Nov 3, 2008

alexmahone

Hint: Write the equation for simple harmonic motion in terms of $\theta$

3. Nov 3, 2008

Andrusko

And use a small angle approximation. That is:

$$sin \theta ~= \theta$$

This is applied when an angle is pretty small.

4. Nov 3, 2008

thank you!