Vibration isolation calculator

Viscously damped SDOF displacement transmissibility at one frequency ratio.

acoustics-isolation.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

This source describes an analytical model. Its quantities and checks are the view.

Scenario	transmissibility
	0.145366
	0.231856

All calculated quantities are listed with the inputs. Switch to Source to inspect the equations.

SCENARIOS / CALCULATED VALUESSAME SOURCE

Change an input to see the consequences.

transmissibility target0.15 ✓ passes

BASELINE INPUTS

ratio3 damping0.1

CALCULATED

transmissibility0.14537

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Vibration isolation
# Scope: Viscously damped SDOF displacement transmissibility at one frequency ratio.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

ratio = 3
damping = 0.1

transmissibility := sqrt((1+(2*damping*ratio)^2)/((1-ratio^2)^2+(2*damping*ratio)^2))

check transmissibility target: transmissibility <= 0.2

scenario alternative: ratio = 2.4

Calculated from your source · not saved

Baseline · Baseline

transmissibility target0.15 ✓ passes

alternative · alternative

transmissibility target0.23 × fails

Illustrative first-order example. Checks are editable requirements, not design standards. The broader topic may require additional equations, data, and validation.

Formula and units

This example uses the following equations. Input names and units match the editable source above.

transmissibility: transmissibility = sqrt((1+(2*damping*ratio)^2)/((1-ratio^2)^2+(2*damping*ratio)^2))

Original worked example

These are the baseline values in the downloadable source. Edits above let you test your own values.

Given

ratio: 3
damping: 0.1

Calculated

transmissibility: 0.145366

Assumptions and limits

Viscously damped SDOF displacement transmissibility at one frequency ratio.

The requirement checks use the limits written in this example. Passing a check does not establish that the model covers every load, material behavior, or operating condition in a real design.

Download this .napkin example ↓

Take it further with your agent

Napkin keeps the inputs, equations, checks and assumptions together in one study. Your agent sets it up; you change the numbers.

Try with Claude ↗

codex 'Use Napkin (https://napkin.engineering/mcp, or the local Napkin plugin) to build a study: Vibration isolation. Inputs: excitation frequency; mount stiffness/damping; mass. Outputs: transmissibility; mount deflection. Model scope: Small-signal vibration and declared sound-propagation conditions. Read napkin_capabilities and the current snapshot. Ask me for the values that matter, label assumptions with units, author .napkin source, validate it and apply it with napkin_source using the current revision, then open the study. Add checks for the limits I supply. Keep unsupported analyses explicit.'

Claude needs the Napkin connector; Codex needs the Napkin plugin. Set up your agent ↗

The broader study

The topic brief below describes the broader scope. The worked example above states the particular calculation it implements.

Inputs: excitation frequency, mount stiffness/damping, mass
Outputs: transmissibility, mount deflection
Modes: calculate, compare, sweep
Drawing: Spectrum and vibration animation

EXECUTABLE WORKED EXAMPLE · FIRST-ORDER MODEL · CHECK THE SCOPE & ASSUMPTIONS