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Math Help - Hint for Inverse Laplace transform

  1. #1
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    Lightbulb Hint for Inverse Laplace transform (SOLVED)

    \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?
    Last edited by Carbon; May 14th 2011 at 09:40 PM.
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  2. #2
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    Quote Originally Posted by Carbon View Post
    \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.
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  3. #3
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    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?
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  4. #4
    Behold, the power of SARDINES!
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    A quadratic is irreducible if if its discriminant is negative.

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