# Help with calculating pendulum problems

1. Jan 14, 2009

### toasted

1. The problem statement, all variables and given/known data
The length of a simple pendulum is .45m, the pendulum bob has a mass of 365 grams, and it is released at an angle of 15o to the vertical.

a.) What is the pendulum bob's speed when it passes through the lowest point of the swing?
b.) What is the total energy stored in this oscillation, assuming no losses?

2. Relevant equations
for part a:
T=2$$\pi$$$$\sqrt{}l/g$$

for part b: I think PE=KE
3. The attempt at a solution

I have attempted a varitety of ways in order to solve this problem however I have been unable to get a reasonable answer. Rather than typing out all of my attempts I will instead give you an idea of what I am trying to do.

For part a I was thinking about trying to figure out the height of the ball when its being pulled back however I wasn't sure about how to determine the height. from there I think I know how to find the speed, especially if I assume the ball is at a height of zero when it is at the bottom of the swing, yet I;m not sure how to find the intial height. Could someone please help?

2. Jan 14, 2009

### LowlyPion

Draw a diagram of the pendulum at the angle θ to the vertical.

Recognize that the distance from the pivot to the height of the pendulum in its raised state is r*cosθ where r is the length of the string.

Since the distance at the bottom to the pivot is r, then that means that the bob has been raised a distance r - r*cosθ or r*(1 - cosθ).

I'll leave you to the mgh and the ½mv².

Good Luck.

3. Feb 1, 2009

### AROD

total energy stored in the oscillation would just be mgh at the heighest point or 1/2 mv^2 at the lowest then, eh?