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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

    Mark44

    Staff: Mentor

    Please don't double post your questions.
     
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