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Stuck on damped pendulum question

  1. Jan 30, 2008 #1
    [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 [tex]b/2m[/tex]?

    2. Relevant equations

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

    x(t) = Asin(wt)

    [tex]w_{0} = \sqrt{g/L}[/tex]

    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 [tex]\Pi[/tex]
    /12, and the amplitude after 1000s [tex]\Pi[/tex]/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


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

    Last edited: Jan 30, 2008
  2. jcsd
  3. Jan 31, 2008 #2

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    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.
  4. Jan 31, 2008 #3
    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
  5. Feb 1, 2008 #4

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    There's no need to to converts to radians, as its the ratio that counts.
  6. Feb 1, 2008 #5
    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.

    Last edited: Feb 1, 2008
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