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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).

    http://www.webassign.net/gianpse3/14-38alt.gif

    (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

    e^(-alpha*t)

    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?

    formulas:
    alpha=b/(2m), b=2*m*a
    w'=sqrt( k/m - b^2/(4m^2) )
    t=(2*pi)/w'

    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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