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Ciel_Phantomhive
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inverse Laplace Transform F(s)= (s^2+2)/(s^2+2s+5)
 2 years ago
 2 years ago
Ciel_Phantomhive Group Title
inverse Laplace Transform F(s)= (s^2+2)/(s^2+2s+5)
 2 years ago
 2 years ago

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satellite73 Group TitleBest ResponseYou've already chosen the best response.1
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 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
think it is partial fractions and then a formula, but really i should just shut up
 2 years ago

Ciel_Phantomhive Group TitleBest ResponseYou've already chosen the best response.0
Yeah but before the use of partial expansion you have to to make it a proper fraction.
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
that i can do
 2 years ago

Ciel_Phantomhive Group TitleBest ResponseYou've already chosen the best response.0
Will it be (s^2+2)/(s+1)^2+4?
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
divide first \[\frac{s^2+2}{s^2+2s+5}=\frac{s^2+2s+52s3}{s^2+2s+5}\] \[=1+\frac{2x3}{s^2+2x+5}\]
 2 years ago

Ciel_Phantomhive Group TitleBest ResponseYou've already chosen the best response.0
what did you divide by?
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
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
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
it is just an algebra trick so you don't have to divide
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
added and subtracted what i needed to match up with the denominator
 2 years ago

Ciel_Phantomhive Group TitleBest ResponseYou've already chosen the best response.0
Oh okay Thanks
 2 years ago

vf321 Group TitleBest ResponseYou've already chosen the best response.0
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...
 2 years ago

Ciel_Phantomhive Group TitleBest ResponseYou've already chosen the best response.0
Oh I have forgotten that, thanks
 2 years ago

vf321 Group TitleBest ResponseYou've already chosen the best response.0
Ah, yes. I just looked at the WolframAlpha link. It did indeed have the delta function.
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
yeah it is in there, rest looks like greek
 2 years ago

vf321 Group TitleBest ResponseYou've already chosen the best response.0
Well the rest falls out of all of that fun stuff from DE class that I don't remember...
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
i know you use partial fractions, and then tables i think
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
but this is when i really should shut up, because i have no idea, although it seems like something i ought to learn
 2 years ago

vf321 Group TitleBest ResponseYou've already chosen the best response.0
I'm pretty sure OP is familiar with relations such as \[\mathcal{L}^{1}\{\frac{1}{s^n}\} = \frac{t^{n1}}{\Gamma (n)}\]But yeah the hard part is just the setup, the rest is looking at the table!
 2 years ago
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