- 4

- 3

**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)

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

**(inverse fourier transorm)**

g(t) =

g(t) =

**F^-1 (G(w))**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?**