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the above equation numerically, you need to approximate the second and first orde d21 dl and dt' respectively) by taking advantages of implicit backward differencing so dt2 order accuracy (i.e. 0 (h)). Then apply the initial conditions as, dI -(t = 0) = 1-. A I(t = 0) = 0,

the above equation numerically, you need to approximate the second and first orde d21 dl and dt' respectively) by taking advantages of implicit backward differencing so dt2 order accuracy (i.e. 0 (h)). Then apply the initial conditions as, dI -(t = 0) = 1-. A I(t = 0) = 0,

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider an electrical circuit with a resistor R, inductor L, and a capacitor C (i.e. RLC circuit) connected in series and energised by a sinusoidal voltage source E. In this system, we want to solve for current I at time t = 1s assuming the governing equation is d²I L- dt2 dI 1 +R +=I = E(t). dt L = 1H, R = 10n, and c = 0.0025 F, E(t) = -0.08 cos 2.5t, and At = 0.01 s. In order to solve the above equation numerically, you need to approximate the second and first order derivatives (i.e. dI and dt' respectively) by taking advantages of implicit backward differencing schemes with first dt2 order accuracy (i.e. 0 (h)). Then apply the initial conditions as, dI A I(t = 0) = 0, (t = 0) = 1. dt
Transcribed Image Text:Consider an electrical circuit with a resistor R, inductor L, and a capacitor C (i.e. RLC circuit) connected in series and energised by a sinusoidal voltage source E. In this system, we want to solve for current I at time t = 1s assuming the governing equation is d²I L- dt2 dI 1 +R +=I = E(t). dt L = 1H, R = 10n, and c = 0.0025 F, E(t) = -0.08 cos 2.5t, and At = 0.01 s. In order to solve the above equation numerically, you need to approximate the second and first order derivatives (i.e. dI and dt' respectively) by taking advantages of implicit backward differencing schemes with first dt2 order accuracy (i.e. 0 (h)). Then apply the initial conditions as, dI A I(t = 0) = 0, (t = 0) = 1. dt
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