Laplace transform

Discussion in 'Math' started by boks, Dec 14, 2008.

  1. boks

    Thread Starter Active Member

    Oct 10, 2008
    218
    0
    1. The problem statement, all variables and given/known data

    Find the laplace transform of t sin(t) and t cos(t), and the inverse transform of \frac{1}{(1+s^2)^2}

    2. The attempt at a solution

    I found the two laplace forms:

    \frac{2s}{(s^2+1)^2}

    and

    \frac{s^2-1}{(s^2+1)^2}

    I guess I'm supposed to use the two laplace transforms to find the inverse of this one, but I don't know how to do that.
     
  2. vvkannan

    Active Member

    Aug 9, 2008
    138
    11
    hi,

    1/(1+s²)² can be written as

    1/2[(s²+1-(s²-1))/(s²+1)²]

    this can be split as
    1/2[(s²+1)/(s²+1)²] - 1/2[(s²-1)/(s²+1)²]

    1/2{[1/(s²+1)] - [(s²-1)/(s²+1)²]}

    inverse of 1/(s²+1) is sin t and the inverese of next term is (t cost).
    Just to bring the denominator in appropriate form we have rearranged as in 1st step.
     
  3. boks

    Thread Starter Active Member

    Oct 10, 2008
    218
    0

    Did you obtain that using separation of variables?
     
  4. vvkannan

    Active Member

    Aug 9, 2008
    138
    11
    just splitting (a - b)/c as a/c - b/c

    where
    a=s²+1 , b = s² - 1 and c= (s² + 1)².
    is this the step you were referring to?
     
  5. boks

    Thread Starter Active Member

    Oct 10, 2008
    218
    0
    Then I'm done with maths for this year. Thanks for helping me with all my problems!
     
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