How Do You Calculate Damping Coefficient in a Pendulum?

[jlew]

[SOLVED] Stuck on damped pendulum question...

Homework Statement

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 $$b/2m$$?

Homework Equations

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

x(t) = Asin(wt)

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

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

 

[Shooting Star]

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

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.

 

[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.

 

[Shooting Star]

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

 

[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 a lot 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!