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Pendulum - find maximum angular displacement

  1. Oct 28, 2009 #1
    1. The problem statement, all variables and given/known data
    A 15-centimeter pendulum moves according to the equation:

    theta=0.2cos8t

    where theta is the angular displacement from the vertical in radians and t is the time in seconds. Determine the maximum angular displacement and the rate of change of theta when t=3 seconds.


    2. Relevant equations
    See, here's where I get stuck. It doesn't seem like I'm given enough information to do ANYTHING with this problem. At first I thought I could find the absolute maximum value by solving for theta at the endpoints and critical numbers, but I don't have any endpoints. Any physics equations I could use go out the window as well, because I have no initial displacement or velocity or any such stuff.


    3. The attempt at a solution
    Insert an hour of frustrated grumbling here, with no results.
     
  2. jcsd
  3. Oct 28, 2009 #2
    Recall from calculus that rate of change is equivalent to the derivative.

    The local extrema of a function are located at the critical points. You can a find a critical point by setting the derivative to 0.

    You should be good to go now.
     
  4. Oct 28, 2009 #3
    Riiiiight, I don't need the absolute, I can just find the local. Thank you very much!! xD
     
  5. Oct 28, 2009 #4
    Okay, so I took the derivative and set it equal to zero, and now I have

    0=-1.6sin8t

    and no theta at all, which is what I am solving for. Also, t would equal 90 (or, since it's in radians, pi over 2), and when you sub it back into the original equation, theta is equal to 0.2 radians, which cannot be the right answer. Any help as to what I'm doing wrong?
     
  6. Oct 28, 2009 #5
    You're absolutely right, the maximum angular displacement is .2.

    Try graphing .2cos(8t) to illustrate the pendulum's behavior.
     
  7. Oct 28, 2009 #6
    It IS 0.2? Phew, thank you. I graphed it, too, I see it now. Thanks for your help!
     
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