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Ciel_Phantomhive

  • 2 years ago

inverse Laplace Transform F(s)= (s^2+2)/(s^2+2s+5)

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  1. satellite73
    • 2 years ago
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    no idea how to do this, but if you can find an answer it should match up with this http://www.wolframalpha.com/input/?i=inverse+laplace+%28s^2%2B2%29%2F%28s^2%2B2x%2B5%29

  2. satellite73
    • 2 years ago
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    think it is partial fractions and then a formula, but really i should just shut up

  3. Ciel_Phantomhive
    • 2 years ago
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    Yeah but before the use of partial expansion you have to to make it a proper fraction.

  4. satellite73
    • 2 years ago
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    that i can do

  5. Ciel_Phantomhive
    • 2 years ago
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    Will it be (s^2+2)/(s+1)^2+4?

  6. satellite73
    • 2 years ago
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    divide first \[\frac{s^2+2}{s^2+2s+5}=\frac{s^2+2s+5-2s-3}{s^2+2s+5}\] \[=1+\frac{-2x-3}{s^2+2x+5}\]

  7. Ciel_Phantomhive
    • 2 years ago
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    what did you divide by?

  8. satellite73
    • 2 years ago
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    i just arranged it so that the power up top was less than the power in the denominator it is either that, or long division

  9. satellite73
    • 2 years ago
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    it is just an algebra trick so you don't have to divide

  10. satellite73
    • 2 years ago
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    added and subtracted what i needed to match up with the denominator

  11. Ciel_Phantomhive
    • 2 years ago
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    Oh okay Thanks

  12. vf321
    • 2 years ago
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    inverse laplace of 1 is the dirac delta - was that in the answer? Because if it wasn't then you may have added a solution...

  13. Ciel_Phantomhive
    • 2 years ago
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    Oh I have forgotten that, thanks

  14. vf321
    • 2 years ago
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    Ah, yes. I just looked at the Wolfram|Alpha link. It did indeed have the delta function.

  15. satellite73
    • 2 years ago
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    yeah it is in there, rest looks like greek

  16. vf321
    • 2 years ago
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    Well the rest falls out of all of that fun stuff from DE class that I don't remember...

  17. satellite73
    • 2 years ago
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    i know you use partial fractions, and then tables i think

  18. satellite73
    • 2 years ago
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    but this is when i really should shut up, because i have no idea, although it seems like something i ought to learn

  19. vf321
    • 2 years ago
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    I'm pretty sure OP is familiar with relations such as \[\mathcal{L}^{-1}\{\frac{1}{s^n}\} = \frac{t^{n-1}}{\Gamma (n)}\]But yeah the hard part is just the setup, the rest is looking at the table!

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