---
title: "A solid, uniform cylindrical buoy of total height \\(H\\), cross-sectional area \\(A\\), and uniform density \\(\\rho_b\\) floats upright in a liquid of density \\(\\rho\\), where \\(\\rho > \\rho_b\\). The buoy is depressed vertically downward by a small distance from its static equilibrium position and released from rest at time \\(t = 0\\). Assuming the liquid is inviscid and resistive drag is negligible, what is the frequency \\(f\\) of the resulting vertical simple harmonic oscillations of the buoy?"
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url: "https://nerd-notes.com/ubq/121005/"
date_modified: "2026-08-23T04:45:08+00:00"
---

# A solid, uniform cylindrical buoy of total height \(H\), cross-sectional area \(A\), and uniform density \(\rho_b\) floats upright in a liquid of density \(\rho\), where \(\rho > \rho_b\). The buoy is depressed vertically downward by a small distance from its static equilibrium position and released from rest at time \(t = 0\). Assuming the liquid is inviscid and resistive drag is negligible, what is the frequency \(f\) of the resulting vertical simple harmonic oscillations of the buoy?

A solid, uniform cylindrical buoy of total height \(H\), cross-sectional area \(A\), and uniform density \(\rho_b\) floats upright in a liquid of density \(\rho\), where \(\rho > \rho_b\). The buoy is depressed vertically downward by a small distance from its static equilibrium position and released from rest at time \(t = 0\). Assuming the liquid is inviscid and resistive drag is negligible, what is the frequency \(f\) of the resulting vertical simple harmonic oscillations of the buoy?

![A grayscale schematic diagram showing a vertical cylindrical buoy floating partially submerged in liquid. A horizontal line represents the liquid surface, with the region below filled with a light gray pattern and labeled \(\rho\). The buoy is drawn as an upright vertical cylinder with total height indicated by a vertical double-headed dimension arrow on the left labeled \(H\). The top flat circular face of the cylinder has a cross-sectional area indicated with label \(A\). The buoy has uniform shading and is labeled \(\rho_b\). The bottom portion of the buoy extends below the liquid surface. A dashed vertical centerline passes through the center of the cylinder. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460308-QdV1KC.jpg)

- **A.** \(f = \dfrac{1}{2\pi} \sqrt{\dfrac{\rho_b g}{\rho H}}\)
- **B.** \(f = \dfrac{1}{2\pi} \sqrt{\dfrac{(\rho - \rho_b) g}{\rho_b H}}\)
- **C.** \(f = \dfrac{1}{2\pi} \sqrt{\dfrac{\rho g}{\rho_b H}}\)
- **D.** \(f = 2\pi \sqrt{\dfrac{\rho g}{\rho_b H}}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121005/*