= Vertical oscillations of a floating cylinder
{title2=$\omega^2=\rho_f gA/m=g/h_0$}
A vertical cylinder of constant cross-sectional <area> $A$, partly immersed to depth $h_0$ in a fluid of <mass density> $\rho_f$, satisfies $mg=\rho_f gAh_0$ by <Archimedes' principle>. A small extra downward displacement $z$ increases the <buoyant force> by $\rho_f gAz$, so $m\ddot z=-\rho_f gAz$. This is <simple harmonic motion> with the displayed <angular frequency> and <oscillation period> $2\pi\sqrt{h_0/g}$. The ideal model neglects fluid added inertia, <drag> and surface effects; it requires partial immersion throughout the motion.
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