Show that the potential energy of a simple pendulum is proportional

[xXmarkXx]

Homework Statement

Show that the potential energy of a simple pendulum is proportional to the square of the angular displacement in the small amplitude limit.

Homework Equations

U=mgh
sin^2wt + cos^2wt=1

The Attempt at a Solution

I can't figure out where to start.

 

[xXmarkXx]

So nobody wants to help a man out? ic...thanks guys!

 

[Mindscrape]

Well, you haven't really given anybody anything that lends a hand towards helping you. What are your thoughts so far?

 

[xXmarkXx]

Well, you haven't really given anybody anything that lends a hand towards helping you. What are your thoughts so far?

Again, i don't know where to start on this one. I know that mgh=mgl(1-cos(theta)) but i don't know how to apply this in the problem. I'm not sure where to go.

 

[Luke1294]

Where did the mgh=mgl(1-cos(theta)) come from?

 

[Mindscrape]

Even if you don't know where to start, you should at least state what you know. For example, you might know that a general oscillator will oscillate with a force $$F = -kx$$, and that potential energy is related to force by $$F = \frac{dU}{dt}$$. Not to say that this helps you out, just the kind of thing that will help identify what level you are at, whether your class is calc based or not and such.

The potential you came up with is correct. What will happen to cos(theta) if theta is relatively small? What is the angular displacement for a simple pendulum?