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!