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!