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Homework Help: Transforming equations

  1. Sep 18, 2007 #1
    I guess this is maybe more algebra than calculus, but it stems from a calculus problem, so I'll stick it here.

    The problem is:

    In the case of the simple harmonic oscillator the solution [to the EOM] may be written at least 3 ways

    x(t) = Acos(wt) + Bsin(wt)
    = Ccos(wt + del)
    = De^(iwt) + Ee^(1wt)

    Express C and del in terms of A and B. Express D and E in terms of A and B.

    What I've got:

    I got the first part, C and del, but I can't figure out how to find D and E. It seems relatively straightforward, I put the A/B eq as the LHS and the D/E eq on the RHS and just applied Euler's Formula to the D term. But I can't figure out how to get the E term in terms of cos and sin.

    Any help please?
     
  2. jcsd
  3. Sep 18, 2007 #2
    Hint: A constant that has the imaginary unit in it is still a constant.
     
  4. Sep 18, 2007 #3
    Yes, I know, but that still doesn't help me get E*e^(wt) in terms of cos and sin.
     
  5. Sep 18, 2007 #4

    Dick

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    D*exp(iwt)+E*exp(wt) is NOT a solution to a simple harmonic oscillator problem in the region of the universe I'm used to. Are you sure you don't mean D*exp(iwt)+E*exp(-iwt)? You certainly can decompose exp(wt) into sin and cos. It's exp(wt)=exp(i(wt/i))=cos(wt/i)+i*sin(wt/i). But if w and t are real, those sin and cos aren't the oscillatory functions you'd expect.
     
  6. Sep 19, 2007 #5
    Yeah, one of my friends just told me "Didn't you get Prof's email? That's a typo!"

    Gr. I KNEW that I wasn't doing it wrong.

    Thanks!
     
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