A lobsterman’s buoy is a solid wooden cylinder of radius r and mass M. It is weighted on one end so that it floats upright in calm sea water, having density . A passing shark tugs on the slack rope mooring the buoy to a lobster trap, pulling the buoy downward a distance x from its equilibrium position and releasing it. Show that the buoy will execute simple harmonic motion if the resistive effects of the water are neglected. (Do this on paper. Your instructor may ask you to turn in this work.) Determine the period of the oscillations.
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