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The following linear differential equation models the charge on the capacitor, q(t), at time t in an RLC series circuit: Ld2q Rdq 1q=E(t). dt2 dtC Find the charge on the capacitor when L = 1 henry, R = 5 ohms, C = 14 farad, and E(t) = 9 − e−t (an electromotive force is turned on at time t = 0 and increases to 9 volts as t → ∞). Assume the initial conditions q(0) = 0 coulombs and i(0) = 0 amperes.
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