# Stuck on damped pendulum question

1. Jan 30, 2008

### jlew

[SOLVED] Stuck on damped pendulum question...

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

A pendulum of length 1.00m is released at an angle of 15.0 degrees. After 1000 seconds, it's amplitude is decreased to 5.50 degrees due to friction. What is the value of $$b/2m$$?

2. Relevant equations

w = $$\sqrt{w_{0}^{2} - (b/2m)^{2}}$$

x(t) = Asin(wt)

$$w_{0} = \sqrt{g/L}$$

3. The attempt at a solution

I have attempted this problem from a few angles, but I don't think I'm on the right track. I am assuming that I must treat the pendulum as a simple harmonic oscillator, making the original amplitude $$\Pi$$
/12, and the amplitude after 1000s $$\Pi$$/32.2. I am just not sure what to do next.

Any help is appreciated, I have a feeling I might be making this a little harder than it has to be, the answer is 1.00 * 10^-3 s^-1

EDIT

I am starting to think I can just get away with using the equation x = Ae$$^-(b/2m)t$$, but it still seems like I do not have enough information to answer this problem yet....

Thanks

Last edited: Jan 30, 2008
2. Jan 31, 2008

### Shooting Star

You are right. You need the ratio of the values of this quantity at two different times, which you do have. The A is a const.

3. Jan 31, 2008

### Gear300

I'm pretty sure you have the right amount of information, although I might be wrong.
A is a constant (your starting amplitude in radians).
The amplitude = 5.50 degrees (convert to radians) at t = 1000 seconds, and so you'd plug into the equation and solve for the ratio.

Last edited: Feb 1, 2008
4. Feb 1, 2008

### Shooting Star

There's no need to to converts to radians, as its the ratio that counts.

5. Feb 1, 2008

### jlew

Thanks for the replies, I was able to solve this question by taking the ratio of x = Ae^-(b/bm)t. I was making this problem ALOT harder than it actually was, mostly because I didn't really understand what the previous formula was solving for. I was originally trying to treat pendulum like a simple harmonic oscillating block, and solving for its natural frequency and angular frequency due to the damping, which is why I was stuck.

Cheers!

Last edited: Feb 1, 2008