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How do you solve this 2nd ODE for a pendulums displacement..

  1. Sep 16, 2015 #1
    ..when it is released from rest with velocity (v0, 0)

    Screen Shot 2015-09-16 at 15.07.22.png

    I can get 1.6.5 but I can't get this:

    Screen Shot 2015-09-16 at 15.08.01.png
     
  2. jcsd
  3. Sep 16, 2015 #2

    Geofleur

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    First, note that ## \tilde{r}(0) = A + B = 0 ##, because the pendulum starts off at the origin. This equation gives ## A = -B ##. Next, calculate the time derivative of ## \tilde{r} ##, evaluate it at time zero, and set it equal to ## v_0 + i(0) = v_0##:

    ## i[(\omega_1-\Omega)A-B(\Omega+\omega_1)] = v_0 ##.

    But the only way this equation could be true is if

    ## (\omega_1 - \Omega)A - B(\Omega+\omega_1)=-i v_0 ##.

    Do you see it? The rest follows by using ## A = -B ##.
     
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