A spar buoy is a cylindrical object that floats with its axis in the vertical direction. When it is disturbed a distance h from its equilibrium position, the magnitude of the restoring force is equal to ρghS, where ρ is the density of the water and S is the cross-sectional area of the cylinder. A certain spar buoy has a mass of 150 kg, a cross-sectional area of 2.50 m², and is floating in seawater, ρ = 1025 kg/m³. What is the frequency of ocean waves which will cause it to resonate? A) 12.9 Hz B) 2.06 Hz C) 7.19 Hz D) 17.1 Hz E) 2.72 Hz

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Quizplus · Accepted Answer

The frequency of resonance can be found using the formula for the natural frequency of a simple harmonic oscillator: $ f = \frac{1}{2\pi} \sqrt{\frac{k}{m}} $, where $ k = \rho g S $ is the restoring force constant. Substituting the given values, $ k = 1025 \times 9.81 \times 2.50 $, and $ m = 150 $, we find $ f \approx 2.06 $ Hz.

A Spar Buoy Is a Cylindrical Object That Floats with Its