# Homework Help: Show that the potential energy of a simple pendulum is proportional

1. Apr 22, 2007

### xXmarkXx

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

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

2. Relevant equations

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

3. The attempt at a solution

I can't figure out where to start.

2. Apr 22, 2007

### xXmarkXx

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

3. Apr 22, 2007

### Mindscrape

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

4. Apr 22, 2007

### xXmarkXx

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.

5. Apr 22, 2007

### Luke1294

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

6. Apr 22, 2007

### 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?