# Pendulum Geometry

1. Oct 29, 2007

### vertabatt

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

What is the height of the object and pendulum bob at the top of the swing, when they have reached their maximum displacement? Keep in mind that the pendulum has a length L and swings through an angle theta.

2. Relevant equations

Trigonometric functions

3. The attempt at a solution
I am trying to find the height, h in order to be able to complete a mechanical energy problem that I am fully able to complete. My problem is that my geometry might be a little rusty and I can't seem to solve for this needed value.

I broke down the diagram into two triangles-- one is isosceles with two sides equal to L which converge to form angle theta.

The other triangle (a right triangle) shares the side opposite theta and has a leg equal to h.

Now, there must be some fancy geometry trick to be able to solve for h in terms of L and theta, but I honestly can't seem to figure it out. I am sure there is a rule for triangles that I am forgetting that will solve this.

2. Oct 29, 2007

### learningphysics

Draw a line from where the pendulum is up at the angle... draw a line from there perpendicular to the vertical (the line along which the pendulum was initially hanging)

use the right triangle formed by the angle theta... the line from the pivot to where the pendulum is up at theta (this is the hypoteneuse with length L)... and the line that you just drew (opposite to theta)...

what is the length of the side adjacent to theta. use this to get h.

3. Oct 29, 2007

### vertabatt

h = L-Lcos(theta)

Thanks!

4. Oct 29, 2007

no prob.