Heart Pacemaker A heart pacemaker, shown in FIGURE 2.7.10, consists of a switch, a b...

Heart Pacemaker A heart pacemaker, shown in FIGURE 2.7.10, 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 Problem 47 in Exercises 2.3, we saw that during the time the electrical stimulus is being applied to the heart, the voltage E across the heart satisfies the linear DE

(a) Let us assume that over the time interval of length t₁, (0, t₁), the switch S is at position P shown in Figure 2.7.10 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 Thus, over the initial charging/ discharging interval the voltage to the heart is actually modeled by the piecewise-defined differential equation

By moving S between P and Q, the charging and discharging over time intervals of lengths t₁ and t₂ is repeated indefinitely. Suppose and and so on. Solve for E(t) for 0 ≤ t ≤ 24.

(b) Suppose for the sake of illustration that R = C = 1. Use a graphing utility to graph the solution for the IVP in part (a) for 0 ≤ t ≤ 24.