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A mass spring system is given by the ODE: 2x′′ +cx′ +8(π^2)x=0 a) What are the values of c ≥ 0 for which the system is: -Overdamped -Critically damped -Underdamped b) Pick a value of c > 0 (note you cannot use c = 0) which is underdamped, and write down a general solution of the system. c) Suppose c = 0, but there is an external force which is given by the periodic extension of F(t) = 4t,  for −1 < t ≤ 1 That is the ODE is given by: 2x′′ +8(π^2)x=F(t), Does resonance occur? d) What is the Fourier series of F given in c)?

A mass spring system is given by the ODE: 2x′′ +cx′ +8(π^2)x=0 a) What are the values of c ≥ 0 for which the system is: -Overdamped -Critically damped -Underdamped b) Pick a value of c > 0 (note you cannot use c = 0) which is underdamped, and write down a general solution of the system. c) Suppose c = 0, but there is an external force which is given by the periodic extension of F(t) = 4t,  for −1 < t ≤ 1 That is the ODE is given by: 2x′′ +8(π^2)x=F(t), Does resonance occur? d) What is the Fourier series of F given in c)?

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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A mass spring system is given by the ODE:

2x′′ +cx′ +8(π^2)x=0

a) What are the values of c ≥ 0 for which the system is:

-Overdamped

-Critically damped

-Underdamped

b) Pick a value of c > 0 (note you cannot use c = 0) which is underdamped, and write down a general solution of the system.

c) Suppose c = 0, but there is an external force which is given by the periodic extension of

F(t) = 4t,  for −1 < t ≤ 1

That is the ODE is given by:

2x′′ +8(π^2)x=F(t), Does resonance occur?

d) What is the Fourier series of F given in c)?

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