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4 7.1 KBps X Page 7 1 25.5 KBps ZOOM + FIGURE 1.3.12 Cubical tank in Problem 13 14. The right-circular conical tank shown in FIGURE 1.3.13 loses water out of a circular hole at its bottom. Determine a different mg tial equation for the height of the water h at time t. The radius of the hole is 2 in, g = 32 ft/s', and the friction/contraction factor introduced in Problem 13 is c = 0.6. FIGURE 1.3.16 Air resistance proportional to square of velocity 8 ft in Problem 17 Aw =Newton's Second Law and Archimedes' Principle 18. A cylindrical barrel s ft in diameter of weight w lb is floating 20 ft in water as shown in FIGURE 1.3.17(a). After an initial depres- sion, 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 `circular hole origin is taken to be on the vertical axis at the surface of the water when the barrel is at rest. Use Archimedes' principle: FIGURE 1.3.13 Conical tank in Problem 14 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 Series Circuits water is 62.4 1b/ft', and that there is no resistance between 15. A series circuit contains a resistor and an inductor as shown in the barrel and the water. FIGURE 1.3.14. Determine a differential equation for the current $/2 i(t) if the resistance is R, the inductance is L, and the impressed $/2 voltage is E(t). surface 00000 .0 0 R (a) (b FIGURE 1.3.14 LR-series circuit in Problem 15 FIGURE 1.3.17 Bobbing motion of floating barrel in Problem 18 26 CHAPTER 1 Introduction to Differential Equations