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Consider the following system of coupled second-order equations, x + 4x1 = x2 x+ 4x2 = 0. Re-write this system of second order equations as a system of first order equations. Compute the solution for the initial condition x1(0) compute the (complex) Jordan normal form for the system. Note: you should find that the solution grows linearly in time which is indicative of a resonance in the system. 1, x(0) = 0, x2(0) = 1, x½(0) = 0. Then

Consider the following system of coupled second-order equations, x + 4x1 = x2 x+ 4x2 = 0. Re-write this system of second order equations as a system of first order equations. Compute the solution for the initial condition x1(0) compute the (complex) Jordan normal form for the system. Note: you should find that the solution grows linearly in time which is indicative of a resonance in the system. 1, x(0) = 0, x2(0) = 1, x½(0) = 0. Then

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 the following system of coupled second-order equations, x + 4x1 = x2 x2 + 4x2 0. Re-write this system of second order equations as a system of first order equations. Compute the solution for the initial condition x1(0) = 1, x1(0) = 0, x2(0) compute the (complex) Jordan normal form for the system. Note: you should find that the solution grows linearly in time which is indicative of a resonance in the system. = 1, x2(0) 0. Then
Transcribed Image Text:Consider the following system of coupled second-order equations, x + 4x1 = x2 x2 + 4x2 0. Re-write this system of second order equations as a system of first order equations. Compute the solution for the initial condition x1(0) = 1, x1(0) = 0, x2(0) compute the (complex) Jordan normal form for the system. Note: you should find that the solution grows linearly in time which is indicative of a resonance in the system. = 1, x2(0) 0. Then
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