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Forced response and Laplace transform

  1. Sep 27, 2012 #1
    1. The problem statement, all variables and given/known data
    d'^2 (y)/dt + 4 (dy/dt) + 4y = -7(e^(-3t)). Here I need to forced response of this differential equation using laplace transform technique.


    2. Relevant equations


    3. The attempt at a solution
    I understand the part of converting each term to each laplace,
    d^2y/dt to Y(s)*s^2, dy/dt to Y(s)*s, y(t) to Y(s), where each term is being converted from f(t) to F(s). I really confused on how to proceed with this question form here :cry:
     
  2. jcsd
  3. Sep 27, 2012 #2

    LCKurtz

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    Unless you have a couple of 0 initial conditions, you need to put them in the transforms of the derivatives. You also need to transform the right side of the DE. Solve the resulting equation for Y(s) and invert it.
     
  4. Sep 29, 2012 #3
    I found out by applying laplace to each factor,

    s^2y(t)+4sy(t)+4y(t)=-7t(t+3)
    s^2y(t)+4sy(t)+4y(t)=-7t(t)-7y(3)
    y(t)(s^2+4s+11)=y(3)

    But from here, I am confused. Since in the question the value of u(t) was given to be e^-3t. Other wise I would have used laplace transform of u(t) which is 1/s.
    Also in the last line, I couldn't factorize the polynomial which is hindering my progress.
    Any help would be whole heartedly appreciated.
     
  5. Sep 29, 2012 #4

    LCKurtz

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    Did you read my reply? Are your initial conditions y(0)=0 and y'(0) = 0 or not? You were using Y(s) for the transform of y(t). You have t's in your transform when they should be s's and y when you should have Y. And where did the t(t+3) on the right side come from? It surely isn't the transform of e^(-3t).
     
  6. Sep 29, 2012 #5

    Ray Vickson

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    L[y'(t)](s) ≠ s*Y(s) and L[y"(t)](s) ≠ s^2*Y(s) in general (although for some special conditions on y(.) these are true). Check your sources!

    RGV
     
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