When a floating body of mass $m$ and cross-sectional area $A$ is pushed down slightly by distance $x$ in a liquid of density $\rho$, the extra buoyant force is $\rho Agx$, which acts as a restoring force. The resulting SHM has $T = 2\pi\sqrt{m/(\rho Ag)}$. For a uniform cylinder: $m = \rho_{\text{body}} \cdot A \cdot h$ (where $h$ is total height), so $T = 2\pi\sqrt{\rho_{\text{body}} h/(\rho g)}$. This is a favorite JEE problem type combining fluid mechanics with oscillations.