- #1
ondine4
- 4
- 3
Hi, let's take this ode:
y''(t) = f(t),y(0)=0, y'(0)=0.
using the FT it becomes:
-w^2 Y(w) = F(w)
Y(w)=( -1/w^2 )F(w)
so i can say that -1/w^2 is the Fourier transorm of the green's function(let's call it G(w)).
then
y(t) = g(t) * f(t)
where
g(t) = F^-1 (G(w)) (inverse Fourier transorm)
how can i solve the integral to find g(t)?
if f(t)=0 for t<0 and f(t)=1 for t>=0 how can i say that y(t)= 1/2t^2?
y''(t) = f(t),y(0)=0, y'(0)=0.
using the FT it becomes:
-w^2 Y(w) = F(w)
Y(w)=( -1/w^2 )F(w)
so i can say that -1/w^2 is the Fourier transorm of the green's function(let's call it G(w)).
then
y(t) = g(t) * f(t)
where
g(t) = F^-1 (G(w)) (inverse Fourier transorm)
how can i solve the integral to find g(t)?
if f(t)=0 for t<0 and f(t)=1 for t>=0 how can i say that y(t)= 1/2t^2?