Question

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

Answer 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

Answer 2

think it is partial fractions and then a formula, but really i should just shut up

Answer 3

Yeah but before the use of partial expansion you have to to make it a proper fraction.

Answer 4

that i can do

Answer 5

Will it be (s^2+2)/(s+1)^2+4?

Answer 6

divide first
\[\frac{s^2+2}{s^2+2s+5}=\frac{s^2+2s+5-2s-3}{s^2+2s+5}\]
\[=1+\frac{-2x-3}{s^2+2x+5}\]

Answer 7

what did you divide by?

Answer 8

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

Answer 9

it is just an algebra trick so you don't have to divide

Answer 10

added and subtracted what i needed to match up with the denominator

Answer 11

Oh okay Thanks

Answer 12

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...

Answer 13

Oh I have forgotten that, thanks

Answer 14

Ah, yes. I just looked at the Wolfram|Alpha link. It did indeed have the delta function.

Answer 15

yeah it is in there, rest looks like greek

Answer 16

Well the rest falls out of all of that fun stuff from DE class that I don't remember...

Answer 17

i know you use partial fractions, and then tables i think

Answer 18

but this is when i really should shut up, because i have no idea, although it seems like something i ought to learn

Answer 19

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!