Source: https://guthlabs.ai/docs/instruments/damped-vibration-response-calculator/implementation/

instrument implementation / implementation-contract

# Damped Vibration Response Calculator implementation

A source-bound implementation contract for Damped Vibration Response Calculator; deployment and executable qualification remain separate.

Status: **VERIFIED_WITH_ERRATA**Lifecycle: **implementation-contract**

## Binding contract

This record describes what an executable surface must bind and validate. It does not claim that a public calculator, package, or production route is deployed.

**Record owner**: Guth Instruments

**Lifecycle**: verified-with-binding-errata

**Evidence ID**: t6-105

**Effect**: Computation or source lookup only

## Input and validation requirements

The instrument breaks at zero mass through division by zero, reaches a validity failure at critical damping, produces a non-real damped frequency when the damping-ratio branch switches to overdamping, and has an unresolved signed-damping convention that can reverse decay into growth.

## Required corrections

````
[
  {
    "vector": 2,
    "field": "logarithmic_decrement / x(π/8)",
    "wrong": "3.0 / -0.1",
    "correct": "4.712389 (=1.5π, in her own working) / -0.009478 (working has the decay factor, field drops it)",
    "cause": "fields contradict own correct working"
  },
  {
    "vector": 3,
    "field": "x(0)",
    "wrong": 0,
    "correct": 0.1,
    "cause": "critically damped x(0)=X=0.1; working even notes the model caveat then ships 0"
  },
  {
    "vector": 4,
    "field": "omega_d / log_decrement / x(0) / x(π/(12√3))",
    "wrong": "2.0 / 2.0 / 0.2 / 0.2",
    "correct": "3.464102 / 3.627599 / 0.173205 / 0.147823",
    "cause": "ENTIRE vector: working computes every value correctly (2√3, 2π/√3, 0.1√3, 0.2e^(-π/6√3)) and every field ships a wrong number"
  }
]
````

## Inspectable interface fixture

The sample below is evidence for interface and validation tests, not a production implementation.

````
{
  "inputs": {
    "k": 100,
    "m": 1,
    "c": 0,
    "X": 0.05,
    "phi": "0 rad",
    "sample_times": [
      "0 s",
      "π/20 s",
      "π/10 s"
    ]
  },
  "expected_outputs": {
    "omega_n": "10 rad/s",
    "zeta": 0,
    "omega_d": "10 rad/s",
    "logarithmic_decrement": 0,
    "sampled_points": {
      "t=0 s": "x=0.05 m",
      "t=π/20 s": "x=0 m",
      "t=π/10 s": "x=-0.05 m"
    },
    "curve_features": {
      "decay_envelope": "x=±0.05 m",
      "roots": "t=(π/2+nπ)/10 s, n integer",
      "successive_extrema": "t=nπ/10 s, x=0.05(-1)^n m"
    }
  },
  "working": "ωn=√(k/m)=√(100/1)=10 rad/s. ζ=c/(2√(km))=0/(2√(100·1))=0. ωd=10√(1−0²)=10 rad/s. δ=2π·0/√(1−0²)=0. Response: x(t)=0.05e^(−0·10t)cos(10t)=0.05cos(10t). At t=0: x=0.05cos(0)=0.05 m. At t=π/20: 10t=π/2, so x=0.05cos(π/2)=0 m. At t=π/10: 10t=π, so x=0.05cos(π)=−0.05 m."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/damped-vibration-response-calculator/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/damped-vibration-response-calculator/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/damped-vibration-response-calculator/qualification/>)

## Sources and evidence

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

- `VERIFIED_LEDGER.json`

- `evidence-tranche6/tranche6-results.json`

- `tranche errata record`