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Differential equation for motion of a pendulum

  1. Apr 13, 2012 #1
    Hello,

    I'm trying to create a model of pendulum motion in Matlab to fit the curve we measured in class, and it has some non-linear components (friction). It looks like the best fit is a sinusoid with an envelope given by a parabola (see attached file).

    The equations of motion are given by:
    [itex]\ddot{\phi}(t) = -k_2\dot{\phi}(t)-k_3\sin(\phi(t))[/itex]

    How this equation can be changed so that the solution of it is a searched sinusoid?

    Thank you.

    // edit: please move this to Differential Equations
     

    Attached Files:

    Last edited: Apr 13, 2012
  2. jcsd
  3. Apr 13, 2012 #2

    mathman

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    The usual approach is to linearize, assuming the angle of the swing is small, so replace sin(φ(t)) by φ(t).
     
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