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The motion of a damped harmonic oscillator is given by d +B= x(t)+kx(t) = 0. dt d²x(t) dt² We restrict the damping parameter ß to be strictly positive, so p > 0. Write the 2nd order ODE as a first order system and classify the fixed point for all possible values of ß and k. Determine the portions of (B,k) where the trivial equilibrium is a node, spiral, etc.

The motion of a damped harmonic oscillator is given by d +B= x(t)+kx(t) = 0. dt d²x(t) dt² We restrict the damping parameter ß to be strictly positive, so p > 0. Write the 2nd order ODE as a first order system and classify the fixed point for all possible values of ß and k. Determine the portions of (B,k) where the trivial equilibrium is a node, spiral, etc.

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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The motion of a damped harmonic oscillator is given by d +B=x (t) +kx(t) = 0. dt d²x(t) dt² We restrict the damping parameter ß to be strictly positive, so ß > 0. Write the 2nd order ODE as a first order system and classify the fixed point for all possible values of ß and k. Determine the portions of (P, k) where the trivial equilibrium is a node, spiral, etc.
Transcribed Image Text:The motion of a damped harmonic oscillator is given by d +B=x (t) +kx(t) = 0. dt d²x(t) dt² We restrict the damping parameter ß to be strictly positive, so ß > 0. Write the 2nd order ODE as a first order system and classify the fixed point for all possible values of ß and k. Determine the portions of (P, k) where the trivial equilibrium is a node, spiral, etc.
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