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Math Help - la place inverse transform

  1. #1
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    la place inverse transform

    hey
    how do we do inverse la place transforms for s/(s-9)(s+8)
    and 9(s+3)/((s+3)^2+81)((s+3)^2+36)?

    thanks in advance
    Last edited by ramzouzy; March 6th 2008 at 10:28 AM. Reason: one extra related problem =S
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  2. #2
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    we would use partial faction decomp.

    this gives us


    \frac{s}{(s-9)(s+8)}=\frac{\frac{9}{17}}{s-9}+\frac{\frac{8}{17}}{s+8} the inverse transform of these are

    \frac{9}{17}e^{9t}+\frac{8}{17}e^{-8t}
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  3. #3
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    thanks for the first one mate but do u know how u would approach the second problem? that one is more important to me
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  4. #4
    Behold, the power of SARDINES!
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    Quote Originally Posted by ramzouzy View Post
    thanks for the first one mate but do u know how u would approach the second problem? that one is more important to me
    You bet...

    Once again we to use partial fracion decomp so

    \frac{9(s+3)}{[(s+3)^2+81][(s+3)^2+36]}=\frac{-1}{5}\frac{(s+3)}{[(s+3)^2+9^2]}+\frac{1}{5}\frac{(s+3)}{[(s+3)^2+6^2]}

    S axis translation theorem backwards we get...

    \mathit{L}(e^{at}f(t)=F(s-a)

    \frac{-1}{5}e^{-3t}\cos(9t)+\frac{1}{5}e^{-3t}\cos(6t)
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  5. #5
    Senior Member Peritus's Avatar
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    You have to know the ROC, to find out the inverse transform. (but I may be wrong).
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