Inverse Laplace Transform Help

  • Thread starter plexus0208
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  • #1
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Homework Statement


Find the unit impulse response for the operator D^4 + I, using the Laplace transform.

Homework Equations



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:

Answers and Replies

  • #2
rock.freak667
Homework Helper
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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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