ODE-26

Damping ratio

Viscous damping ratio.

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GoverningDamping ratio

Governing equation

\\zeta=c/(2\\sqrt{km})

where

c: c (N·s/m)
k: k (N/m)
m: m (kg)
z: Damping ratio (—)

Lecture brief

Historical brief

Exponential decay, the harmonic oscillator, SIR epidemics, Lotka–Volterra and Bessel are the first solvable ODEs of nature and populations. The lab is rate, period and phase portrait in closed form. This sheet (ODE-26 — Damping ratio) is the form associated with Damping ratio. Working symbols: $c$ , $k$ , $m$ $\rightarrow$ $z$ . Viscous damping ratio. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

z

from

c

k

m

in Differential equations via

\\zeta=c/(2\\sqrt{km})

Viscous damping ratio. Use it when a real differential equations question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

c = 4.000\,\mathrm{N·s/m}

k = 40.000\,\mathrm{N/m}

m = 2.000\,\mathrm{kg}

, the governing relation

\\zeta=c/(2\\sqrt{km})

yields

z = 0.224\,\mathrm{—}

. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

c c4 N·s/mk k40 N/mm m2 kg

Outputs

Damping ratio z0.224 —

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Narration of this film

One governing identity, SI units, a single sweep on the sheet.

Viscous damping ratio. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube