Source: https://guthlabs.ai/docs/instruments/elastic-spring-potential-energy-calculator/

instrument / verified-clean

# Elastic/Spring Potential Energy Calculator

The current ledger marks this instrument verified clean within the source-bound verification corpus.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Inspectable records

[01**Overview**Purpose and lifecycle](<https://guthlabs.ai/docs/instruments/elastic-spring-potential-energy-calculator/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/elastic-spring-potential-energy-calculator/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/elastic-spring-potential-energy-calculator/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/elastic-spring-potential-energy-calculator/qualification/>)

## Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

**Area**: Physics — Kinematics/Projectiles/Orbits, Forces/Energy/Momentum, Rotational Dynamics, Gravitation, Oscillations/Waves, Optics, E&M Fields, Relativity, Quantum, Statistical Thermo

**Tranche**: tranche-4

**Evidence ID**: t4-155

**Ledger rows**: 1

No ledger note is attached.

## Review findings

The spring-energy formula is valid, but the instrument's advertised combined spring+gravity capability is unsupported by the listed formula and inputs. Clarify whether x is measured from the unstretched or equilibrium position, and either remove the combined-gravity claim or specify U_total = ½kx² + mgh together with m, h, g, units, and a height reference.

### Formula and scope findings

- U=½kx² is correct for elastic potential energy in an ideal linear spring, with x measured from the spring's unstretched/equilibrium reference position.

- The stated computation includes combined spring+gravity potential-energy problems, but the specification provides no gravity formula, mass, height, or gravitational-field input. The listed formula computes spring energy only.

- The reference position for x is not explicitly defined; using total length instead of displacement from the unstretched position would be incorrect.

### Unit assumptions

- k must be in N/m and x must be in meters for U to be returned in joules.

- x may be positive for extension or negative for compression; squaring makes the spring energy nonnegative.

- If combined gravity energy is added later, mass must be in kilograms, height in meters, and g in m/s²; gravitational potential energy would require a defined reference and sign convention.

## Boundary hardening

**BREAK_CLAIMED** · SELF_FLAGGED

The extreme finite inputs k=10^308 N/m and x=10^154 m produce a mathematically finite value of 5×10^615 J but overflow ordinary JavaScript numeric arithmetic to Infinity.

## Errata and corrections

No applied erratum is attached to this unique-name record.

## Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

````
{
  "inputs": {
    "k": 200,
    "k_unit": "N/m",
    "x": 0.15,
    "x_unit": "m"
  },
  "expected_outputs": {
    "U": 2.25,
    "U_unit": "J"
  },
  "working": "U = ½kx² = ½(200)(0.15²) = 100(0.0225) = 2.25 J"
}
````

## Related workflows

No source-defined multi-instrument workflow membership is recorded.

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json · VERIFIED_CLEAN`

- `evidence-tranche4/tranche4-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`