s/2 |s/2 surface }y(1) (a) (b) FIGURE 1.3.17 Bobbing motion of floating barel in Problem 18
A cylindrical barrel s feet in diameter of weight w lb is
floating in water as shown in Figure 1.3.17(a). After an initial
depression the barrel exhibits an up-and-down bobbing motion
along a vertical line. Using Figure 1.3.17(b), determine a
differential equation for the vertical displacement y(t) if the
origin is taken to be on the vertical axis at the surface of the
water when the barrel is at rest. Use Archimedes’ principle:
Buoyancy, or upward force of the water on the barrel, is
equal to the weight of the water displaced. Assume that the
downward direction is positive, that the weight density of water
is 62.4 lb/ft3, and that there is no resistance between the barrel
and the water.
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