Although I've been looking everywhere, I have been unable to find an answer to my question so here it is. For a driven damped pendulum the equation of motion in dimensionless units is,
$$\alpha(\omega,\theta,t)=-c\ \omega -\sin \theta +F(t).$$
My question is obtaining my next step $\omega(t + \Delta t)$. I know what to do for time $t$ and $\omega$, but not for $\theta$. The fourth order RK method can be found pretty much anywhere
$$\omega(t+ \Delta t) = \omega(t) + (k_1 +2k_2 +2k_3 + k_4)*\Delta t/6, $$
and I am specifically confused on what to enter for $\theta$ in the $k_1, k_2$. . . calculations. The first one is easy but I'm unsure on the rest:
$$k_1 = \alpha(\omega(t),\ \theta(t),\ t) \\ k_2=\alpha(\omega(t) + k_1\Delta t/2,\ \theta(t) + \ ???,\ t +\Delta t/2) \\ k_3=\alpha(\omega(t) + k_2\Delta t/2,\ \theta(t) + \ ???,\ t +\Delta t/2) \\ k_4=\alpha(\omega(t) + k_3\Delta t,\ \theta(t) + \ ???,\ t +\Delta t).$$
From here solving for the next $\theta(t+\Delta t)$ is simple enough I just need help knowing what to do the above equation. It seems like all the examples that I've seen show examples for only two variables and not three.