An RLC circuit with L = 1 h of inductance, R = 40 of resistance, and C = 0.25 f of capacitance has an initial charge of 1 c on the capacitor and an initial current 0 Amps. 5 V DC is impressed on the system. The system can be modeled by the following initial value problem: q" +4q' + 4q = 5,q (0) = 1, i (0) = 0 a. Solve the initial value problem. You may use any method you would like. (I recommend undetermined coefficients.) b. Describe the circuit as overdamped, underdamped, or critically damped. Explain how you know. c. Describe the long-term, steady-state solution for this system. Write a brief explanation. d. Identify the plot that best illustrates this system.

An RLC circuit with L = 1 h of inductance, R = 40 of resistance, and C = 0.25 f of capacitance has an initial charge of 1 c on the capacitor and an initial current 0 Amps. 5 V DC is impressed on the system. The system can be modeled by the following initial value problem: q" +4q' + 4q = 5,q (0) = 1, i (0) = 0 a. Solve the initial value problem. You may use any method you would like. (I recommend undetermined coefficients.) b. Describe the circuit as overdamped, underdamped, or critically damped. Explain how you know. c. Describe the long-term, steady-state solution for this system. Write a brief explanation. d. Identify the plot that best illustrates this system.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 17EQ

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