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

الأصل · EN

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 θ = -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.