Consider a battery of constant voltage E 0 that charges the capacitor shown in Figure 7.3.10. Divide equation (20) by L and define 2 λ = R / L and ω 2 = 1/ LC. Use the Laplace transform to show that the solution q ( t ) of q ″ + 2 λq ′ + ω 2 q = E 0 / L subject to q (0) = 0, i (0) = 0 is q ( t ) = { E 0 C [ 1 − e − λ t ( cosh λ 2 − ω 2 t + λ λ 2 − ω 2 sinh λ 2 − ω 2 t ) ] , λ > ω , E 0 C [ 1 − e − λ t ( 1 + λ t ) ] , λ = ω , E 0 C [ 1 − e − λ t ( cos ω 2 − λ 2 t + λ ω 2 − λ 2 sin ω 2 − λ 2 t ) ] , λ < ω . Figure 7.3.10 Series circuit in Problem 35
Consider a battery of constant voltage E 0 that charges the capacitor shown in Figure 7.3.10. Divide equation (20) by L and define 2 λ = R / L and ω 2 = 1/ LC. Use the Laplace transform to show that the solution q ( t ) of q ″ + 2 λq ′ + ω 2 q = E 0 / L subject to q (0) = 0, i (0) = 0 is q ( t ) = { E 0 C [ 1 − e − λ t ( cosh λ 2 − ω 2 t + λ λ 2 − ω 2 sinh λ 2 − ω 2 t ) ] , λ > ω , E 0 C [ 1 − e − λ t ( 1 + λ t ) ] , λ = ω , E 0 C [ 1 − e − λ t ( cos ω 2 − λ 2 t + λ ω 2 − λ 2 sin ω 2 − λ 2 t ) ] , λ < ω . Figure 7.3.10 Series circuit in Problem 35
Solution Summary: The author explains that the solution of the expression q′′+2lambda
Consider a battery of constant voltage E0 that charges the capacitor shown in Figure 7.3.10. Divide equation (20) by L and define 2λ = R/L and ω2 = 1/LC. Use the Laplace transform to show that the solution q(t) of q″ + 2λq′ + ω2q = E0/L subject to q(0) = 0, i(0) = 0 is
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Bundle: A First Course in Differential Equations with Modeling Applications, Loose-leaf Version, 11th + WebAssign Printed Access Card for Zill's ... Problems, 9th Edition, Single-Term
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