1. Consider the harmonic oscillator equation: d²y dy m +b + ky = 0 dt² dt a. Turn this second-order equation into a system of first-order equations b. Find the trace and determinant of the corresponding coefficient matrix for the system.

1. Consider the harmonic oscillator equation: d²y dy m +b + ky = 0 dt² dt a. Turn this second-order equation into a system of first-order equations b. Find the trace and determinant of the corresponding coefficient matrix for the system.

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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Question

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1. Consider the harmonic oscillator equation:
d² y dy
m + b + ky = 0
dt² dt
a. Turn this second-order equation into a system of first-order equations
b. Find the trace and determinant of the corresponding coefficient matrix for the system.

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c. If you had extra-physical powers and could make a spring with a negative spring constant (but still
positive values of mass and the damping coefficient), what would that do to the classification of
the origin in the phase plane of the system?

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