Q:

Electrical Circuit with Fourier Transform

I'm working in my Electrical Circuits homeworks. One of the exercises says: "Use the Fourier Transform method to calculate \$v_0(t)\$"
The circuit is this:

where \$v_g=36sgn(t)\$, and \$sgn(t)\$ is the sign of \$t\$ (it returns 1, -1 or 0). Well, my problem is the following. I consulted my table of Fourier Transforms and I found that $$V_g(\omega)=36\cdot \dfrac{2}{j\omega}$$
However, I don't know how to calculate \$\omega\$. I need it in order to calculate the \$V_g\$ and also \$Z_C\$. I know that, if, for example \$v_g(t)=A\sin(kt)\$ then \$k=\omega\$. But in this case I'm completely lost.
How can I do it? Thanks in advance!

A:

However, I don't know how to calculate ω

There's no reason to calculate \$\omega\$.  Your approach should be to find the frequency domain representation of the output voltage, \$V_o(j \omega)\$, and transform that back to the time domain.
In the frequency domain and by voltage division
$$V_o(j\omega) = V_g(j\omega)\dfrac{60k\Omega||\frac{1}{j\omega 2\mu F}}{12k\Omega + 60k\Omega||\frac{1}{j\omega 2\mu F}} $$

