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Engineering · L4 · Single-DOF vibration response by damping ratio

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How a spring-mass-damper system's free-vibration response changes across underdamped, critical, and overdamped regimes.

by @openstemUpdated Engineering
Displace mass, release(free vibration)Compute ζ = c / (2√(km))ζ < 1?Underdamped:oscillates at ω_d = ωₙ√(1−ζ²)amplitude decays exponentiallyζ = 1?Critically damped:fastest return, no overshootOverdamped (ζ > 1):slow return, no oscillationApply sinusoidal forcing at ωCompute r = ω / ωₙr ≈ 1?Resonance:amplitude peaks near 1/(2ζ)Away from resonance:amplitude bounded and modestYesNoYesNoYesNo

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