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Please Help (damped pendulum)

  1. Nov 26, 2004 #1
    Please Help!!!(damped pendulum)

    A physical pendulum consists of an L = 70 cm long, 100 g mass, uniform wooden rod hung from a nail near one end (Fig. 14-38). The motion is damped because of friction in the pivot. The damping force is approximately proportional to d(theta)/dt. The rod is set in oscillation by displacing it 15° from its equilibrium position and releasing it. After 10 seconds, the amplitude of the oscillation has been reduced to 4° . Assume that the angular displacement can be written as

    theta= A*e^(-alpha*t)*cos(w'*t).


    (a) Find alpha

    (b) Find the approximate period of the motion.

    (c) Find how long it takes for the amplitude to be reduced to 1/2 of its original value.

    Don't I need b to find alpha, since damping force is proportional to dtheta/dt, or F=b(dtheta/dt)?
  2. jcsd
  3. Nov 26, 2004 #2
    The formula shows that the amplitude changes with time


    The other bits of the formula are the initial amplitude A, and the oscillating part (the cos term)

    You know that the amplitude decreases from 15° to 4° in ten seconds, so you have:

    e^(-10 alpha) = 4 / 15
  4. Nov 26, 2004 #3
    Can someone verify if I have found the period corectly?

    alpha=b/(2m), b=2*m*a
    w'=sqrt( k/m - b^2/(4m^2) )

    I found the k/m to be 3/2(g/L), where L is the length of the rod. Then I plugged everything in.
  5. Nov 27, 2004 #4
    anyone, please?
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