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Simple partial fractions help (warning complex analysis :P )

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trickae
#1
Apr27-07, 01:58 AM
P: 85
1. The problem statement, all variables and given/known data
the question can be ignored - it involves laplace and Z transforms of RLC ckts.

Vc(s) =          0.2
           -----------------
             s^2 + 0.2s + 1
find the partial fraction equivalent such that it is :
  -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
      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
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lalbatros
#2
Apr27-07, 03:06 AM
P: 1,235
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
#3
Apr27-07, 03:24 AM
P: 85
sorry dude i'm still a little confused.

thats just a rounding error from the J term.

lalbatros
#4
Apr27-07, 04:39 AM
P: 1,235
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.
trickae
#5
Apr28-07, 03:38 PM
P: 85
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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