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The given figure illustrates a cylindrical buoy floating in water with a mass density $.$ Assume that the center of mass of the

buoy is deep enough so that the buoy motion is primarily vertical. The buoy mass is $m$ and the diameter is $D.$ Archimedes's

principle states that the buoyancy force acting on a floating object equals the weight of the liquid displaced by the object.

NOTE: This is a multi$-$part question. Once an answer is submitted, you will be unable to return to this part.

Compute the period of oscillation if the buoy diameter is $2\mathrm{.}3$ ft and the buoy weighs $1200$ lb $.$ Take the mass density of fresh water to

be $=1\mathrm{.}94$ slug$/$ft$3.$

The period of oscillation is determined to be

$($x$)$ s $.$