1 -2- 0 2 3 6. An RLC circuit with 1 Henry of inductance, 70 of resistance, and 0.1 f of capacitance is turned on with 5V DC after 3 seconds. The circuit initially has 0 q of charge and no current. The circuit is modeled by the following initial value problem: q" +7q' + 10q = 5u3(t), q (0) = 0 q'(0) = 0 a. Solve this differential equation using Laplace transforms. b. Is this system overdamped, underdamped, or critically damped? c. Which of the following graphs best shows the behavior of the system? 2- 2 2 4 4 ~ 6 6 6 8 8 8 10 10 10

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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6. An RLC circuit with 1 Henry of inductance, 702 of resistance, and 0.1 f of capacitance
is turned on with 5V DC after 3 seconds. The circuit initially has 0 q of charge and no
current. The circuit is modeled by the following initial value problem:
q" +7q' + 10q = 5u3(t),
q (0) = 0 q'(0) = 0
a. Solve this differential equation using Laplace transforms.
b.
Is this system overdamped, underdamped, or critically damped?
c. Which of the following graphs best shows the behavior of the system?
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Transcribed Image Text:1 -2- 0 2 3 6. An RLC circuit with 1 Henry of inductance, 702 of resistance, and 0.1 f of capacitance is turned on with 5V DC after 3 seconds. The circuit initially has 0 q of charge and no current. The circuit is modeled by the following initial value problem: q" +7q' + 10q = 5u3(t), q (0) = 0 q'(0) = 0 a. Solve this differential equation using Laplace transforms. b. Is this system overdamped, underdamped, or critically damped? c. Which of the following graphs best shows the behavior of the system? 2- 2 2 4 4 6 6 6 8 8 8 10 10 10
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