• Support PF! Buy your school textbooks, materials and every day products Here!

Green's Function using Laplace Transformation

  • Thread starter dspampi
  • Start date
  • #1
16
0
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
 

Answers and Replies

  • #2
33,262
4,963
Please don't double post your questions.
 

Related Threads on Green's Function using Laplace Transformation

  • Last Post
Replies
3
Views
537
Replies
6
Views
928
  • Last Post
Replies
1
Views
834
Replies
0
Views
1K
Replies
7
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
3
Views
1K
Replies
8
Views
9K
  • Last Post
Replies
7
Views
20K
  • Last Post
Replies
1
Views
13K
Top