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Laplace of F(ks)

  1. May 6, 2014 #1
    1. The problem statement, all variables and given/known data
    Compute the inverse laplace transform of F(ks)


    2. Relevant equations



    3. The attempt at a solution

    $$L^{-1} (F(ks)) = \frac{f}{|k|} \left( \frac{t}{k} \right)$$

    Correct?
     
  2. jcsd
  3. May 6, 2014 #2

    Mark44

    Staff: Mentor

    Why do you think you need the absolute value of k?

    What do you get from ##\mathcal{L}(f(t/k))##, using the definition?
     
  4. May 6, 2014 #3
  5. May 6, 2014 #4
    You could just the fact that ##\mathscr{F}[f](\lambda)=\frac{1}{\sqrt{2\pi}}\mathscr{L}[f](i\lambda)## if we assume that ##f(x)=0## for ##x<0##.

    Where the Fourier Transform is the following ##\mathscr{F}[f](\lambda)=\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}f(x)e^{-ix\lambda}dx##

    It should now be clearly what the inverse Laplace transform of the Fourier transform of a function is.
     
  6. May 7, 2014 #5
    I did a simple question. I hoped a yes or not...
     
  7. May 7, 2014 #6
    Your answer is correct. Sorry about earlier, I mistook the F to be the Fourier transform.
     
  8. May 8, 2014 #7
    Ok, thankyou!
     
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