1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    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!

Green's Function using Laplace Transformation

  1. Nov 16, 2011 #1
    I was wondering if someone could help me go through a simple example in using Green's Function.

    Lets say:
    x' + x = f(t)
    with an initial condition of x(t=0,t')=0;

    Step 1 would be to re-write this as:
    G(t,t') + G(t,t') = [itex]\delta[/itex](t-t')

    then do you multiply by f(t')[itex]\oint[/itex]dt' ?
    which I would believe would give me:

    s G(s) + G(s) = e^-st

    and G(s) = [itex]\frac{1}{s+1}[/itex] e^-st'
    then giving me my G(t,t') = e^-(t-t') * U(t-t') ?

    Not sure if that is the expected Green's function or if I screwed up somewhere.

    Also, if f(t) = U(t-1), what would be the system's response?
    * U fxn is a Heaviside step function
  2. jcsd
  3. Nov 16, 2011 #2


    Staff: Mentor

    Please don't double post your questions.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook