1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Inverse Laplace Transform Help

  1. Jan 27, 2014 #1
    1. The problem statement, all variables and given/known data

    Is there a way to evaluate [itex]L^{-1}(\frac{F(s)}{s + a})[/itex]? I'm sure if it can be evaluate.

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Jan 27, 2014 #2


    User Avatar
    Homework Helper

    It depends on what [itex]F[/itex] is. If [itex]F[/itex] has no singularities then the inverse transform
    \mathcal{L}^{-1}\left(\frac{F(s)}{s + a}\right) = \frac{1}{2\pi i}\int_{c-i\infty}^{c + i\infty} \frac{F(s)e^{st}}{s+a}\,ds
    (where [itex]c \in \mathbb{R}[/itex] is such that there are no singularities of [itex]F(s)/(s+a)[/itex] to the right of the line [itex]\mathrm{Re}(s) = c[/itex]) reduces to the residue of [itex]\dfrac{F(s)e^{st}}{s+a}[/itex] at [itex]s = -a[/itex], which is [itex]F(-a)e^{-at}[/itex].
  4. Jan 27, 2014 #3

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Use convolution: if
    [tex] f(t) = L^{-1}[F(s)](t),[/tex]
    [tex] L^{-1} \left( \frac{F(s)}{s+a} \right) (t) = \int_0^t f(t-\tau) e^{-a \tau} \, d \tau.[/tex]
  5. Feb 1, 2014 #4
    So if you have no idea what one of the functions in the frequency domain is and you get something like

    inverse Laplace transform( F(s)G(s) )

    and you know what G(s) of is but F(s) is not given then you have no way to evaluate the expression?
  6. Feb 1, 2014 #5

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Of course. If I give you two different F(s), you will get two different answers.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted