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Transposition as part of a laplace transform

  1. Jan 17, 2013 #1
    I am doing a laplace transform as part of a coursework assignment. I have some example transpositions that are relevant to the question I am answering but I can't see how the author has got from one arrangement to the next.



    2. Relevant equations

    He has given

    1/(s^2(τs+1)) = 1/(τs^2(s+1/τ))

    Is there a rule of transposition I don't know about ? How has he created two instances of τ and made 1/τ ? I know I could follow it blindly but I'd really like to know how he got there.

    Thank you in advance
     
  2. jcsd
  3. Jan 17, 2013 #2

    LCKurtz

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    Science Advisor
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    When you use partial fractions you are looking for factors like ##s^2## or ##(s+a)## in the denominator. Your denominator has ##\tau s + 1## as a factor. To get it into the ##s+a## form, you factor out the ##\tau## getting ##\tau(s+\frac 1 \tau)##. The ##\tau## out in front doesn't hurt anything and what is left is in the proper form to expand in partial fractions to find the inverse.
     
  4. Jan 17, 2013 #3

    Mark44

    Staff: Mentor

    Questions about Laplace transforms should be posted in the Calculus & Beyond section, not in the Precalc section. I am moving this thread to that section.
     
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