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Inverse Laplace Transform Help

  1. Apr 14, 2010 #1
    1. The problem statement, all variables and given/known data
    Find the unit impulse response for the operator D^4 + I, using the Laplace transform.

    2. Relevant equations

    3. The attempt at a solution
    w^(4) + w = δ(t)

    s^4W + W = 1

    W = 1 / (s^4 +1)

    Now, I need to find the inverse laplace transform of W. But I don't know how to simplify W. Should I use partial fractions? If so, how do I factor the denominator?

    (Note: In the first line "^(4)" refers to the fourth derivative with respect to t.
    Last edited: Apr 14, 2010
  2. jcsd
  3. Apr 14, 2010 #2


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    Homework Helper

    you could replace 1 with -i2 where i is the imaginary unit. But you may need to convert that to a better form in the final solution.
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