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: Laplace transformation

  1. Nov 27, 2008 #1
    1. The problem statement, all variables and given/known data
    fing the laplace transformation of f(t) where
    -1 if 0<t<2
    f(t)= e^3t if 2<t<4
    2t if 4<t

    2. Relevant equations

    3. The attempt at a solution

    I can get to the part where f(t) = -1 + (e^3t +1)u(t-2) + (2t-e^3t)u(t-4)
    then I get lost ...Any help is appreciated. Thank you all in advance
  2. jcsd
  3. Nov 28, 2008 #2
    Hi Karmel,

    First note that the -1 you have there should be -u(t); also, a minor point, but I'll assume u(t) is the Heaviside function restricted to t>0 (since f is only defined on t>0).

    Your task now is to work with the formula [tex]g(t-a)u(t-a)\mapsto e^{-as}F(s)[/tex] to take the Laplace transform of f(t). For example, we may rewrite the second term as

    [tex](e^{3t} + 1)u(t-2) = (e^6e^{3(t-2)} + 1)u(t-2)[/tex],

    and so by the above formula this transforms to [tex]e^{-2s}\left(e^6\frac{1}{s-3} + \frac{1}{s}\right)[/tex].

    Your turn. Show us your work if you get stuck.
    Last edited: Nov 28, 2008
  4. Nov 28, 2008 #3
    Okay so by using the examples from the book and the above example for the last part of the above problem I get and if Im right it will be luck!

    (2t-e^3t)u(t-4) = (2t-(e^12)(e^3(t-4))u(t-4) which transforms into e^-4s(-e^12((1/s-3)+(2/s^2))

    so assuming that this part is right. Do I leave the answer as is or do I need to multiply throughout and see if I can add anything and simplyfy it..

  5. Nov 29, 2008 #4
    Almost, but you haven't completely made the factor multiplied by u(t-4) look like a function g(t-4) like in formula I gave above. We need to write it as

    [tex](2t - e^{3t})u(t - 4) = (2(t - 4) + 8 - e^{12}e^{3(t - 4)})u(t - 4)[/tex].

    Once you have transformed each term of f(t), then you have found the Laplace transform of f(t), as required.
  6. Nov 30, 2008 #5
    Thank you so much for the help and assuming I havent made any errors I do believe I have finally arrivied at the right answer. Once again thank you karmel
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook