I have the following equation:
$$m \frac{d^2 x}{dt^2} = -Kx - \alpha \frac{dx}{dt} + f(t) $$
Which I introduced into Mathematica as:
eqn = m D[x[t], {t, 2}] == -K x + f[t] - a D[x[t], t]
I want to take the Fourier transform of this equation to get (after simplyfing terms):
$$ x(\omega) [ - m \omega^2 + i \omega \alpha + K] = f(\omega)$$
(There might be a prefactor missing because I defined the Fourier transform as the inverse Fourier transform of the one that Mathematica uses but that is not important).
In order to do that I tried:
FourierTransform[f[t], t, \[Omega]]
But the output that I get is just:
FourierTransform[ m x''[t] == -K x + f[t] - a x'[t], t, \[Omega]]
It seems that Mathematica doesn't know how to do the Fourier transform of the functions $x(t)$ and $f(t)$ without their explicit form. Is there any way to do this directly with the built in functions of Mathematica?
