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

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satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1no 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

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

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

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

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

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

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1i just arranged it so that the power up top was less than the power in the denominator it is either that, or long division

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

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

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

vf321
 2 years ago
Best ResponseYou've already chosen the best response.0inverse laplace of 1 is the dirac delta  was that in the answer? Because if it wasn't then you may have added a solution...

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

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

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

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

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

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

vf321
 2 years ago
Best ResponseYou've already chosen the best response.0I'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!
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