# Fourier transform of ODE

1. Nov 27, 2005

### sachi

we need to find the F.T of
f(t) = 0 for t<0
f(t) = exp(-at) for t>=0
where a is a real positive constant
and F(w) = the integral w.r.t t between minus infinity and plus infinity of [exp(iwt)*f(t)]

which turns out to be 1/(a-iw)

we now have the ODE L*dI/dt + RI = f(t)
where L,R are constants represeting resistance and inductance. we need to show that the fourier transform of I(t) is 1/(a-iw)(R-Liw) which is again straightforward. We need to find I(t). I have sepearated the F.T of I(t) using partial fractions and used the inverse fourier transform, but I'm not sure how to evaluate the integrals.
thanks very much for your help