Consider a mass-spring system with $m = 1$, no damping, and $k = 4$. Find the general form of the mass’ motion if there is no forcing. Now suppose that we apply an external force $F(t) = 3\cos^3(\omega t)$ for a constant $\omega$. Show that there are two values of $\omega$ at which resonance occurs, and ﬁnd both.
$m = 1$
$k = 4$
$my'' + ky = 0$
$y'' +4y = 0$
$y(t) = c_1\cos (2t) + c_2\sin (2t)$
Now I'm unsure how to show/find the two values for resonance. I know the equation is
$y'' + 4y = 3\cos^3(\omega t)$
but what does that tell me?