anonymous
  • anonymous
inverse Laplace Transform F(s)= (s^2+2)/(s^2+2s+5)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
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
anonymous
  • anonymous
think it is partial fractions and then a formula, but really i should just shut up
anonymous
  • anonymous
Yeah but before the use of partial expansion you have to to make it a proper fraction.

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anonymous
  • anonymous
that i can do
anonymous
  • anonymous
Will it be (s^2+2)/(s+1)^2+4?
anonymous
  • anonymous
divide first \[\frac{s^2+2}{s^2+2s+5}=\frac{s^2+2s+5-2s-3}{s^2+2s+5}\] \[=1+\frac{-2x-3}{s^2+2x+5}\]
anonymous
  • anonymous
what did you divide by?
anonymous
  • anonymous
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
anonymous
  • anonymous
it is just an algebra trick so you don't have to divide
anonymous
  • anonymous
added and subtracted what i needed to match up with the denominator
anonymous
  • anonymous
Oh okay Thanks
anonymous
  • anonymous
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...
anonymous
  • anonymous
Oh I have forgotten that, thanks
anonymous
  • anonymous
Ah, yes. I just looked at the Wolfram|Alpha link. It did indeed have the delta function.
anonymous
  • anonymous
yeah it is in there, rest looks like greek
anonymous
  • anonymous
Well the rest falls out of all of that fun stuff from DE class that I don't remember...
anonymous
  • anonymous
i know you use partial fractions, and then tables i think
anonymous
  • anonymous
but this is when i really should shut up, because i have no idea, although it seems like something i ought to learn
anonymous
  • anonymous
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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