I just encountered a problem involving lift and oscillations where I found the following differential equation: $$\ddot y = -\frac{ \rho gA}{m}y = -\omega^2 y$$
What's the relation between $\ddot y$, $y$ and $\omega$? Does $\ddot y = -\omega^2y $ or $\ddot y =\omega^2y$ apply in all situations? If yes, what's the reasoning behind it? I know it makes sense in terms of the units but what's the physical reason behind it?