Serway & Jewett — Oscillatory Motion: Problem 41

Review. A lobsterman’s buoy is a solid wooden cylinder of radius \(r\) and mass \(M\). It is weighted at one end so that it floats upright in calm seawater, having density \(\rho\). A passing shark tugs on the slack rope mooring the buoy to a lobster trap, pulling the buoy down a distance \(x\) from its equilibrium position and releasing it. (a) Show that the buoy will execute simple harmonic motion if the resistive effects of the water are ignored. (b) Determine the period of the oscillations.