1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Partial fraction

  1. Sep 27, 2006 #1
    This is actually part of a larger problem of solving a diff EQ by use of a laplce transform, but it's the partial fraction part that I'm stuck on.

    [tex]\frac{1}{s^2(s^2+w^2)} = \frac{A}{s}+\frac{B}{s^2}+\frac{C*s+D}{s^2+w^2}[/tex]

    Good so far?

    If I then multiply through by the common denominator I get

    EQ.2[tex]1 = A*s(s^2+w^2) + B(s^2+w^2) + s^2(C*s+D)[/tex]

    So then I set s=0

    [tex]1=B*w^2 \longrightarrow B=1/w^2 [/tex]

    Then using the quadratic equation, I find that the roots of s^2+w^2 are +/- jw

    letting s=jw I end up with

    [tex]1 = -jC*w^3 - Dw^2[/tex]

    this is where I get stuck, I'm not sure how to find C and D at this point.

    Note: I just noticed a mistake in EQ.2,
     
    Last edited: Sep 27, 2006
  2. jcsd
  3. Sep 27, 2006 #2
    you can equate the various bits, ie the coefficients of the quadratic linear and constant terms. you cut out a bit of that with s=0 which is a good trick but u need the other way to get all the constants (if only in terms of w)

    ie [tex]{s^2}(C*s + D) = 0[/tex]

    i think
     
  4. Sep 27, 2006 #3
    Thanks for the reply, but I'm not really sure what you are saying.
     
  5. Sep 27, 2006 #4
    You can get two equations for [itex]C[/itex] and [itex]D[/itex] by letting [itex]s=\pm i\omega[/itex]. You can then solve for [itex]C[/itex] and [itex]D[/itex].

    By the way if you want to know a quick way to do this you can say the following:

    [tex]
    \frac{1}{xy} = \frac{1}{x-y}\left\{\frac{1}{y}-\frac{1}{x}\right\}
    [/itex]

    So if I choose [itex]x=s^2+\omega^2[/itex], and [itex]y=s^2[/itex] then your initial fraction can be cast directly into the form on the RHS of your equation.
     
    Last edited: Sep 27, 2006
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Partial fraction
  1. Partial Fractions (Replies: 5)

  2. Partial Fractions (Replies: 4)

  3. Partial fractions (Replies: 3)

  4. Partial fractions (Replies: 4)

  5. Partial fractions (Replies: 2)

Loading...