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Laplace transform

  1. Jun 7, 2009 #1
    1. The problem statement, all variables and given/known data

    s2-5 / s3+4s2+3s


    2. Relevant equations

    find the inverse laplace transform


    3. The attempt at a solution
    for the denominator, it can be factored out to s(s+3)(s+1) or one could complete the square and thus the denominator would be s(s+2)2-1. neither of this help in finding the laplace transform
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jun 7, 2009 #2

    rock.freak667

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    Homework Helper

    Factor it into s(s+3)(s+1), then split into partial fractions.
     
  4. Jun 7, 2009 #3
    haha, thanks. just as i received your post, i actually figured it out. but thank you for taking the time to look at my problem
     
  5. Jun 7, 2009 #4
    another problem

    1. The problem statement, all variables and given/known data
    3s / (s+1)4


    2. Relevant equations
    find the inverse laplace


    3. The attempt at a solution
    i used partial fractions to split it up into A/(s+1) + B/(s+1)2 +c/(s+1)3 +D/(s+1)4

    which in turn gives me A(s+1)3 + B(s+1)2 + C(s+1) + D = 3s
    i plugged in s=-1 to get D=-3, i dunno how to find A, B or C (sad i know) maybe its just a late night and my brain isnt working well because i cant seem to figure it out
     
  6. Jun 7, 2009 #5

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    As long as you have distinct first order factors, you can put in a single value for x and immediately reduce to one coefficient. With powers or irreducible quadratics, its not so trival but still not hard.

    Probably easiest: put in 3 more values for s, say s= 0, s= 1, and s= 2, to get 3 linear equations in A, B, C. They won't reduce to three separated equations but still you can solve them.

    Harder: go ahead and multiply everything out: [itex]A(s^3+ 3s^2+ 3s+ 1)+ B(s^2+ 2s+ 1)+ C(s+ 1)- 3[/itex][itex]= As^3+ 3As^2+ 3As+ A+ Bs^2+ 2Bs+ B+ Cs+ C- 3= 3s[/itex].

    Now combine "like terms" to get 3 equations for A, B, and C.
     
  7. Jun 7, 2009 #6
    3s = 3(s+1) - 3
     
  8. Jun 7, 2009 #7
    Yes, it looks like a shifting property would be the best to tackle this problem.
     
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