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Homework Help: Laplace Transform question

  1. Nov 23, 2012 #1
    1. The problem statement, all variables and given/known data

    this one stumped me..

    d^2y/dt^2 +ωy=ksin((√ω)t)

    y(∏/4)=0, y'(∏/4)=0

    3. The attempt at a solution

    → (s^2 + ω)U(s)= LT {ksin((√ω)(T+∏/4)} is as far as i can get (i know what to do with the left hand side once i get the LT of the right hand side but i dont know what to do with the sin value)
  2. jcsd
  3. Nov 23, 2012 #2


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    Science Advisor

    What is "T"? Did you mean "t"?

    I presume you know the definition:
    [tex]L(f(t))= \int_0^\infty e^{-st}f(s)dx[/tex]

    Here that woud be
    [tex]\int_0^\infty e^{-st}(k sin(\sqrt{\omega}(t+ \pi/4))dt[/tex]

    The substitution v= [itex]\sqrt{\omega}(t+ \pi/4)[/itex] reduces that to a fairy straight forward "integration by parts" but you should also have formulas for the Laplace transform of sin(x) as well as for f(x+ a) in terms of the Laplace transform of f(x).
  4. Nov 24, 2012 #3
    well, i would normally use tau but i couldnt find symbol, so i just used T to distinguish from t

    doing this by integration by parts ends with a complicated (a) (from sin at) that is impossible to break down into to a/s^2+a^2 (LT formula) ...if it were just sin√wt then i get it..but i am missing some step
    Last edited: Nov 24, 2012
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