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Inverse Laplace Transforms

  1. Jun 1, 2014 #1
    1. The problem statement, all variables and given/known data
    f(s) = -5s/S^2+9


    2. Relevant equations
    I think
    f(t) cosωt = f(s) s/s^2+ω^2


    3. The attempt at a solution
    ω=3

    Answer
    -5cos(3t)

    Can anyone tell me if I did this correctly? I think I did but just want to make sure, if not can you tell me what I did wrong?

    Thanks
     
  2. jcsd
  3. Jun 1, 2014 #2

    CAF123

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    Gold Member

    There is not really much of a problem statement there but, going by the title, I think you are after the inverse laplace transform of ##f(s) = -5 \frac{s}{s^2+9}##. Yes, your result is correct. $$\mathcal{L}^{-1} f(s) \equiv Y(t) = -5 \cdot \mathcal{L}^{-1}\left( \frac{s}{s^2+9}\right) = -5 \cos 3 t$$
     
  4. Jun 1, 2014 #3
    I just wanted to verify my answers, I dont have asolutions manual and want to make sure I am doing the problems correctly.

    Thank you
     
  5. Jun 1, 2014 #4

    Ray Vickson

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    Science Advisor
    Homework Helper

    Your answer is wrong for what you WROTE, which was
    [tex] f(s) = -\frac{5s}{s^2}+9[/tex]
    but it would be correct if you had written
    [tex] f(s) = -\frac{5s}{s^2+9}[/tex]
    In text you would write this using parentheses: f(s) = -5s/(s^2+9). Such a simple step to avoid confusion!
     
  6. Jun 1, 2014 #5
    I am sorry, the way you wrote it the second way is the way it was supposed to be written.. guess I need to learn to make proper equations.

    Thanks again
     
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