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20. For the harmonic oscillator with mass m = 1, spring constant k = 4, and damping coefficient b = 5, (a) compute the eigenvalues and associated eigenvectors; (b) for each eigenvalue, pick an associated eigenvector V and determine the solu- tion y(t) with Y(0) = V; (e) for each solution derived in part (b), plot its solution curve in the yu-phase plane;

20. For the harmonic oscillator with mass m = 1, spring constant k = 4, and damping coefficient b = 5, (a) compute the eigenvalues and associated eigenvectors; (b) for each eigenvalue, pick an associated eigenvector V and determine the solu- tion y(t) with Y(0) = V; (e) for each solution derived in part (b), plot its solution curve in the yu-phase plane;

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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20. For the harmonic oscillator with mass m = 1, spring constant k = 4, and damping coefficient b = 5, (a) compute the eigenvalues and associated eigenvectors; (b) for each eigenvalue, pick an associated eigenvector V and determine the solu- tion y(t) with Y(0) = V; (c) for each solution derived in part (b), plot its solution curve in the yv-phase plane; (d) for each solution derived in part (b), plot its y(t)- and v(t)-graphs; and (e) for each solution derived in part (b), give a brief description of the behavior of the mass-spring system.
Transcribed Image Text:20. For the harmonic oscillator with mass m = 1, spring constant k = 4, and damping coefficient b = 5, (a) compute the eigenvalues and associated eigenvectors; (b) for each eigenvalue, pick an associated eigenvector V and determine the solu- tion y(t) with Y(0) = V; (c) for each solution derived in part (b), plot its solution curve in the yv-phase plane; (d) for each solution derived in part (b), plot its y(t)- and v(t)-graphs; and (e) for each solution derived in part (b), give a brief description of the behavior of the mass-spring system.
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