Inverse Laplace Transform Help

1. Apr 14, 2010

plexus0208

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. Apr 14, 2010

rock.freak667

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.