Simple partial fractions help (warning complex analysis :P )

  1. 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 (Text):

    Vc(s) =          0.2
               -----------------
                 s^2 + 0.2s + 1
     
    find the partial fraction equivalent such that it is :
    Code (Text):

      -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 (Text):

          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
     
    Last edited: Apr 27, 2007
  2. jcsd
  3. 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 ?
     
    Last edited: Apr 27, 2007
  4. sorry dude i'm still a little confused.

    thats just a rounding error from the J term.
     
  5. I just wanted to say that, except for decimals, you did it correctly.
    You should solve the last equation and conclude.
     
  6. 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?

    https://www.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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