CALCULATORS / SPRINGS AND ELASTIC ENERGY

Lumped spring-mass resonance calculator

Lumped equivalent spring/mass resonance; not internal spring surge modes.

springs-surge.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

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

Scenario	frequencyHz	separation
	35.5881	7.11763
	31.831	6.3662

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.

frequency separation target7.12 ✓ passes

BASELINE INPUTS

rate5 N/mmeffectiveMass0.1 kgexcitation5 Hz

CALCULATED

frequency35.588 Hz

separation7.1176

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Spring natural-frequency screening
# Scope: Lumped equivalent spring/mass resonance; not internal spring surge modes.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

rate = 5 N/mm
effectiveMass = 0.1 kg
excitation = 5 Hz

frequency := sqrt(rate/effectiveMass)/(2*pi) [Hz]
separation := frequency/excitation

check frequency separation target: separation >= 3

scenario alternative: rate = 4 N/mm

Calculated from your source · not saved

Baseline · Baseline

frequency separation target7.12 ✓ passes

alternative · alternative

frequency separation target6.37 ✓ passes

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.

frequency: frequency = sqrt(rate/effectiveMass)/(2*pi) [Hz]
separation: separation = frequency/excitation

Original worked example

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

Given

rate: 5 N/mm
effective mass: 0.1 kg
excitation: 5 Hz

Calculated

frequency: 35.5881 Hz
separation: 7.11763

Assumptions and limits

Lumped equivalent spring/mass resonance; not internal spring surge modes.

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: Spring natural-frequency screening. Inputs: rate; effective mass; operating frequency. Outputs: natural frequency; separation from excitation. Model scope: Linear elasticity within the declared material range. 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: rate, effective mass, operating frequency
Outputs: natural frequency, separation from excitation
Modes: calculate, compare, sweep
Drawing: Spring deformation

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