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1. Use Laplace Transforms to determine the function modeling the current in an RLC circuit with L 10 Henries, R= 20 ohms, C = 0.02 Farads, the initial charge is Q(0) = 0, the initial current is I(0) = 0, there is an electromotive force forcing the RLC circuit via the voltage function E(t) = 10 sin(t), and then, at t = 27 seconds, the battery is turned off, letting the current alternate naturally through the circuit. Use the fact the differential 1 d²Q dQ equation L + R +2 = (1-u2 (t)) 10 sin(t - 2) to find the solution for Q(t) and dt dt² then take its derivative to find I(t). Be careful of discontinuities when taking the derivative. Graph both Q and I using your favorite software and attach them.

1. Use Laplace Transforms to determine the function modeling the current in an RLC circuit with L 10 Henries, R= 20 ohms, C = 0.02 Farads, the initial charge is Q(0) = 0, the initial current is I(0) = 0, there is an electromotive force forcing the RLC circuit via the voltage function E(t) = 10 sin(t), and then, at t = 27 seconds, the battery is turned off, letting the current alternate naturally through the circuit. Use the fact the differential 1 d²Q dQ equation L + R +2 = (1-u2 (t)) 10 sin(t - 2) to find the solution for Q(t) and dt dt² then take its derivative to find I(t). Be careful of discontinuities when taking the derivative. Graph both Q and I using your favorite software and attach them.

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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1. Use Laplace Transforms to determine the function modeling the current in an RLC circuit with L=10 Henries, R= 20 ohms, C = 0.02 Farads, the initial charge is Q(0) = 0, the initial current is I(0) = 0, there is an electromotive force forcing the RLC circuit via the voltage function E(t) = 10 sin(t), and then, at t = 27 seconds, the battery is turned off, letting the current alternate naturally through the circuit. Use the fact the differential 1 equation L + R +2= (1 - U2 (t)) 10 sin(t - 27) to find the solution for Q(t) and d²Q dQ dt² then take its derivative to find I(t). Be careful of discontinuities when taking the derivative. Graph both Q and I using your favorite software and attach them. dt
Transcribed Image Text:1. Use Laplace Transforms to determine the function modeling the current in an RLC circuit with L=10 Henries, R= 20 ohms, C = 0.02 Farads, the initial charge is Q(0) = 0, the initial current is I(0) = 0, there is an electromotive force forcing the RLC circuit via the voltage function E(t) = 10 sin(t), and then, at t = 27 seconds, the battery is turned off, letting the current alternate naturally through the circuit. Use the fact the differential 1 equation L + R +2= (1 - U2 (t)) 10 sin(t - 27) to find the solution for Q(t) and d²Q dQ dt² then take its derivative to find I(t). Be careful of discontinuities when taking the derivative. Graph both Q and I using your favorite software and attach them. dt
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