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Driven Harmonic Oscillator - Mathematical Manipulation of Equations

  1. Feb 1, 2009 #1
    1. The problem statement, all variables and given/known data and the attempt at a solution

    Please see attached.

    I'm not so sure if my problem lies with the physics or the mathematics. I have the distinct feeling that it's the latter and that I'm missing something elementary, but truly have no idea how to proceed.

    Any advice will be appreciated.

    Attached Files:

  2. jcsd
  3. Feb 1, 2009 #2
    Express the forcing function in terms of


    then separate the real and imaginary parts of the solution for x. The real part is the desired solution.
  4. Feb 2, 2009 #3
    I'm afraid I don't quite know what you mean...How do I write

    [tex]F(t)=F_0 \sin{\omega t}[/tex]

    in terms of

    [tex]e^{i\omega t}[/tex]

  5. Feb 2, 2009 #4
    Use the Euler Equation




    If you are not familiar with this, try using the identity for sin(A+B) and cos(A+B).
  6. Feb 2, 2009 #5
    I really appreciate the help, but please bear with me as I try to wrap my head around this. I do know the Euler equation, but my understanding is that only the real part relates to SHM and since x as well as F(t) are given as functions of sine (not cosine), I don't know how to "bridge the gap" so to speak. I've tried using the identities for sine and cosine as you mention, but end up with massively intimidating equations involving [tex]\sin\phi[/tex] and [tex]\cos \phi[/tex] which doesn't really help as I don't know how to get rid of either...
  7. Feb 2, 2009 #6
    After using the sin(A+B) and cos(A+B) identities, equate the coeffecients:

    The sin(omega*t) coefficients on the right side of the equation are equal to F0 and the cos(omega*t) coefficients are equal to zero.
    Last edited: Feb 2, 2009
  8. Feb 4, 2009 #7
    Finally the light! :biggrin: Thank you! I'm going to play with this and hopefully I won't get stuck again :smile:
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