Hint for Inverse Laplace transform

**Carbon** · May 14th 2011, 08:05 PM

$\frac{8s^2-4s+12}{s^3+4s}$

Can someone give me a hint as to the best way to attack this one? I am not sure what to do with the top. Do I need to complete a square?

**TheEmptySet** · May 14th 2011, 08:09 PM

Originally Posted by Carbon

$\frac{8s^2-4s+12}{s^3+4s}$

Can someone give me a hint as to the best way to attack this one? I am not sure what to do with the top. Do I need to complete a square?

Factor and use termwise division to get

$\frac{8s^2}{s(s^2+4)}+\frac{-4s}{s(s^2+4)}+\frac{12}{s(s^2+4)}$

note for the last one that you may need partial fractions if you do not know the convolution theorem.

**Carbon** · May 14th 2011, 08:24 PM

Thanks a lot.

I will use partial fractions. One think I'm rusty on is irreducible fractions. Is $s^2+4$ irreducible? How do I know if something is irreducible?

**TheEmptySet** · May 14th 2011, 08:30 PM

A quadratic is irreducible if if its discriminant is negative.

$b^2-4ac=0-4(1)(4)=-16$

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