Relationship between Period of a pendulum and length

[Dynamite]

Homework Statement

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

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.

 

[alexmahone]

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

 

[Andrusko]

And use a small angle approximation. That is:

$$sin \theta ~= \theta$$

This is applied when an angle is pretty small.

 

[Dynamite]

thank you!