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Damped Simple Harmonic Motion

  1. Oct 27, 2005 #1
    I'm having trouble with this problem. I want to get it into a form with cos but I'm stumped.
    The solution for damped simple harmonic motion is given by
    x = (e^(-rt/2m))(C_1*e^(iw't)+C_2*e^(-iwt))
    If x = Acos phi at t = 0, find the values of C_1 and C_2 to show that x'=(approx) -w'Asinphi at t = 0 only if r/m is very small or phi =(approx) pi/2.

    Where w = omega and phi = angle phi and i=complex variable x' = 1st derivative

    Any ideas or help would be really appreciated.
    Last edited: Oct 27, 2005
  2. jcsd
  3. Oct 31, 2005 #2


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    Staff: Mentor

    exp (ix) = cos x + i sin x, and exp (-ix) = cos x - i sinx

    Expand the exponentials and then rearrange the coefficents for cos x and i sinx.
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