Heart Pacemaker A heart pacemaker, shown in Figure 3.1.14,
Chapter 3, Problem 3.1.45(choose chapter or problem)
Heart Pacemaker A heart pacemaker, shown in Figure 3.1.14, consists of a switch, a battery, a capacitor, and the heart as a resistor. When the switch S is at P, the capacitor charges; when S is at Q, the capacitor discharges, sending an electrical stimulus to the heart. In in Exercises 2.3 we saw that during this time the electrical stimulus is being applied to the heart, the voltage E across the heart satisfies the linear D . (a) Let us assume that over the time interval of length t1, 0 t t1, the switch S is at position P shown in Figure 3.1.14 and the capacitor is being charged. When the switch is moved to position Q at time t1 the capacitor discharges, sending an impulse to the heart over the time interval of length t2: t1 t t1 t2. Thus over the initial charging/discharging interval 0 t t1 t2 the voltage to the heart is actually modeled by the piecewise-defined differential equation . dE dt 0, 1 RC E, 0 t t1 t1 t t1 t2
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