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arXiv · 1404.4763

On the Instability and Critical Damping Conditions, $kτ= 1/e$ and $kτ= π/2$ of the equation $\dotθ = -k θ(t-τ)$

Z. Jane Wang
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Abstract

In this note, I show that it is possible to use elementary mathematics, instead of the machinery of Lambert function, Laplace Transform, or numerics, to derive the instability condition, $k τ= π/2$, and the critical damping condition, $kτ= 1/e$, for the time-delayed equation $\dotθ = -k θ(t-τ)$. I hope it will be useful for the new comers to this equation, and perhaps even to the experts if this is a simpler method compared to other versions.

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Z. Jane Wang. 2014-04-18. On the Instability and Critical Damping Conditions, $kτ= 1/e$ and $kτ= π/2$ of the equation $\dotθ = -k θ(t-τ)$. https://arxiv.org/abs/1404.4763

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