A uniform solid cylindrical buoy of length \(L\), cross-sectional area \(A\), and uniform density \(\rho_b\) floats upright in static equilibrium in a liquid of density \(\rho\), where \(\rho > \rho_b\). The buoyant force exerted on the buoy when submerged to a depth \(h\) has magnitude \(F_B = \rho A g h\). The buoy is pushed vertically downward by a small distance from its equilibrium position and released from rest at time \(t = 0\). Taking the downward displacement from equilibrium to be \(z\), which of the following pairs of expressions correctly gives the second-order differential equation of motion for \(z(t)\) and the angular frequency \(\omega\) of the resulting vertical oscillations?