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Partial fractions (for laplace)

  1. Dec 13, 2009 #1
    1. The problem statement, all variables and given/known data
    This problem is killing me.

    I need to bust this thing up using partial fractions.

    2zqwxmb.jpg


    2. Relevant equations


    3. The attempt at a solution

    I'm leaning towards it being separated like this. Is this correct?
    fnfne1.jpg

    If it is, I'm not exactly sure what I'm supposed to do next.
     
    Last edited: Dec 13, 2009
  2. jcsd
  3. Dec 13, 2009 #2
    145s/ [(s+2j)(s-2j)(s-2+3j)(s-2-3j)]
    Make sure above is correct .. now

    [145s / (s-2j)(s-2+3j)(s-2-3j) ]*1/ [(s+2j)]
    +
    [145s / (s+2j)(s-2+3j)(s-2-3j) ]*1/ [(s-2j)]
    +
    [145s / (s-2j)(s+2j)(s-2-3j) ]*1/ [(s-2+3j)]
    +
    [145s / (s-2j)(s+2j)(s-2+3j) ]*1/ [(s-2-3j)]

    I believe what I did above should be self explanatory. Now next step is to substitute s=-2j to [145s / (s-2j)(s-2+3j)(s-2-3j) ]
    s=2j to [145s / (s+2j)(s-2+3j)(s-2-3j) ]
    s = 2-3j in the third, and s=2+3j .. so on, You leave one of the simplest possible factor in the denominator taking all others to the numerator and then substituting the root.

    See if that works :biggrin:
     
  4. Dec 13, 2009 #3
    I'll try that, thanks :approve:
     
  5. Dec 13, 2009 #4
    Answering your question in the OP, you had that correct. But, I just wanted to share a new tool I discovered in Calc III class which I think is very helpful for partial fractions.
     
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