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# Differential Equations : Harmonic Oscillator with Damping Coefficient

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22. Consider a harmonic oscillator with mass m = 1, spring constant k = 1, and damping coefficient b = 4. For the initial position y(O) = 2, find the initial velocity for which y(t) > 0 for all t and y(t) reaches 0.1 most quickly. [Hint: It helps to look at the phase plane first.]

Differential Equations
From Phase plane for Linear Systems with Real Eigenvalues

##### Solution Summary

Differential Equations and an Harmonic Oscillator with a Damping Coefficient are investigated. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.

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