- #1
dspampi
- 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
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