simple partial fractions help (warning complex analysis :P )

trickae

1. The problem statement, all variables and given/known data
the question can be ignored - it involves laplace and Z transforms of RLC ckts.

Code:

Vc(s) =          0.2
           -----------------
             s^2 + 0.2s + 1

find the partial fraction equivalent such that it is :

Code:

  -j(0.1005)     +    j (0.1005)
--------------    ------------------
s + 0.1-(0.995)    s + 0.1 + j(0.995)

2. Relevant equations

none

3. The attempt at a solution

Code:

      0.2                      A                     B
---------------  =  ---------------------  +  -------------------
s^2 + 0.25 + 1      s + (0.1 - j(0.995)))     s + (0.1 + j(0.995))

0.2 = A(s + 0.1 + j(0.995)) + B(s + (0.1 - j0.995))

0.2 = As + A(0.1 + j(0.995)) + Bs + B(0.1 - j0.995)

so As + Bs = 0
or (A + B) = 0
or A = -B
so
0.2 = j(0.995A) - j(0.995B)

somethings not right - if i evaluate this I don't get anywhere near the answer

*lalbatros*

Well, check this:

(s + 0.1 - I 0.995)(s + 0.1 + I 0.995) = 1.00002 + 0.2 s + s²

there is a small inaccuracy ... but nothing more.
Solve your last equation and turn to another exercice.

What does that become:

0.2 = j(0.995A) - j(0.995B)

if A=-B ?

trickae

sorry dude i'm still a little confused.

thats just a rounding error from the J term.

*lalbatros*

I just wanted to say that, except for decimals, you did it correctly.
You should solve the last equation and conclude.

trickae

thanks man i got it now - actually my next question is a little off topic ... but how did i get a post stuck in this thread?

http://physicsforums.com/showthread.php?t=166823&page=2

I don't understand the thread whatsover. ANyways thanks for the help i actually got the answer i'l put it up when i get home.

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lalbatros	Well, check this: (s + 0.1 - I 0.995)(s + 0.1 + I 0.995) = 1.00002 + 0.2 s + s² there is a small inaccuracy ... but nothing more. Solve your last equation and turn to another exercice. What does that become: 0.2 = j(0.995A) - j(0.995B) if A=-B ?

trickae	sorry dude i'm still a little confused. thats just a rounding error from the J term.

lalbatros	simple partial fractions help (warning complex analysis :P ) I just wanted to say that, except for decimals, you did it correctly. You should solve the last equation and conclude.