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Homework Help: Easy Laplace?

  1. Feb 15, 2010 #1
    1. The problem statement, all variables and given/known data

    Find the inverse Laplace of:

    [tex]X(s) = \frac{3}{s^2 - 6}[/tex]

    I am kind of stuck on this one. I am pretty sure this is not sinusoidal. Can I even use partial fractions on this?

    Just a hint here :smile:
  2. jcsd
  3. Feb 15, 2010 #2


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    It's probably in a table. Or consider the bottom a difference of squares: [tex]s^2-(\sqrt{6})^2[/tex] and use partial fractions.
  4. Feb 15, 2010 #3

    [tex]X(s) =\frac{3}{s^2 - 6}= \frac{3}{(s+\sqrt{6})(s- \sqrt{6})}= \frac{a}{s + \sqrt6} + \frac{b}{s - \sqrt6}[/tex]

    [tex]\Rightarrow a = \left( \begin{matrix}\frac{3}{(s+\sqrt{6})(s- \sqrt{6})}*({s + \sqrt6})\end{matrix} \right)_ {s\rightarrow -\sqrt6}=\frac{-3}{2\sqrt6}[/tex]


    [tex]\Rightarrow b = \left( \begin{matrix}\frac{3}{(s+\sqrt{6})(s- \sqrt{6})}*({s - \sqrt6})\end{matrix} \right)_ {s\rightarrow +\sqrt6}=\frac{3}{2\sqrt6}[/tex]
    Last edited: Feb 15, 2010
  5. Feb 15, 2010 #4


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    If you wanted you could just use

    [tex]L(sinh(kt))= \frac{k}{s^2-k^2}[/tex]

    But partial fractions work just as well.
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