Damping and Mechanical Transients — Cheat sheet

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Core rule

ωn=k/m,\omega_n=\sqrt{k/m}, ζ=c2mk.\zeta=\frac{c}{2\sqrt{mk}}.

Watch for

Increasing damping beyond critical can slow the dominant return mode. Claims about “fastest settling” depend on initial data and a chosen settling criterion; distinguish that design question from the root classification.