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Homework Help: Laplace issue

  1. Sep 10, 2008 #1
    1. The problem statement, all variables and given/known data
    M[tex]\ddot{X}[/tex](t)+c[tex]\dot{X}[/tex](t)+kx(t) =f(t)
    Initial Conditions:
    x(0) = .02
    -Use laplace transform to convert the ordinary differential equation in the time domain to an algebraic equation in the frequency domain.
    -Derive the transfer Function G(S) = [tex]\frac{X(S)}{F(S)}[/tex]

    2. Relevant equations

    3. The attempt at a solution
    mS[tex]^{2}[/tex]X(S) - .02MS + CSX(S) - .02C + KX(S) = F(S)

    [mS[tex]^{2}[/tex] - CS+K]X(S) = F(S) +.02MS - .02C

    X(S) = F(S) +.02MS - .02C / mS[tex]^{2}[/tex] - CS+K

    This is where I get confused.
    1. Should I of divided out the M in the beginning?(i.e. k/m, c/m..)
    2. At this point do I need partial fractions to go further?
    Last edited: Sep 10, 2008
  2. jcsd
  3. Sep 10, 2008 #2


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    Homework Helper

    Recheck this line. You should not have any minus sign.

    A pity you aren't given the unknowns explicitly. Because using the quadratic formula to get the factors looks really complicated. I really don't see how to use partial fractions since you're not given F(s).
  4. Sep 10, 2008 #3
    yeah at 3am I might make mistakes...
    it should be
    X(S) = [F(S) +.02MS + .02C] / [MS^2 + CS+K]

    Now I see X(S) = [F(S)/M]/[S^2 + CS/M+K/M] + [.02S + .02C/M]/[S^2 + CS/M+K/M]

    from here I need some more help.. I think C/M and K/M mean something else..
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