we need to find the F.T of(adsbygoogle = window.adsbygoogle || []).push({});

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

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Fourier transform of ODE

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**