LIVEdataset aec-bench@releasetasks 552models 18last submission … · built …
mechanicalwith-tool

Vibration Transmissibility

Calculates force transmissibility for a damped single-degree vibration isolation system from forcing frequency, natural frequency, and damping ratio. The template reports frequency ratio, transmissibility, and isolation efficiency.

with-tool: The model is given an executable Python calculator script.

Standards

ISO 20816

Tags

deterministicisolationmechanicaltransmissibilityvibration

How this task is generated

One template produces many comparable benchmark tasks while keeping the scoring contract fixed.

  1. 01

    Template

    The reusable contract shown on this page.

  2. 02

    Scenario

    An archetype and site context are sampled.

  3. 03

    Difficulty tier

    Inputs may be hidden at harder tiers.

  4. 04

    Task prompt

    The model responds with the declared outputs.

Parameters

Inputs the model receives, and the outputs it is scored on.

Inputs

3 inputs

Always given

Included directly in every task prompt.

3

  • Forcing frequency

    forcing_frequency_hz

    Excitation or forcing frequency

    0.1 – 200 Hz

  • Natural frequency

    natural_frequency_hz

    Isolator natural frequency

    0.1 – 100 Hz

  • Damping ratio

    damping_ratio

    Viscous damping ratio

    0 – 1

Scored outputs

3 outputs

Frequency ratio

frequency_ratio

Ratio of forcing frequency to natural frequency

Scores if within ±3% of the reference value.

Transmissibility

transmissibility

Damped force transmissibility

Scores if within ±3% of the reference value.

Isolation efficiency pct

isolation_efficiency_pct

Isolation efficiency

Scores if within ±3% of the reference value.

Difficulty

Each template is sampled at three tiers. Harder tiers may hide inputs, forcing the model to infer them from the scenario description.

All inputs remain visible at every tier

For this template, difficulty scales through parameter and scenario ranges rather than hidden information.

easy:
All parameters given for a pump isolator
medium:
All parameters given across isolation systems
hard:
All parameters given for precision equipment isolation

Task bundle

The exact instruction and parameter contract used to generate this task, pinned to the published library source.

/workspace

  • instruction.md
  • vibration-transmissibility_calc.py

Teal lines show Jinja input conditions, not task visibility policy. A line renders only when that input or tool is visible.

1You are a senior mechanical engineer specializing in vibration isolation.2 3## Problem4 5Calculate vibration transmissibility for a damped single-degree isolation system.6 7## Given8 9| Parameter | Value | Unit |10|-----------|-------|------|11| Forcing frequency | {{ forcing_frequency_hz }} | Hz |12| Natural frequency | {{ natural_frequency_hz }} | Hz |13| Damping ratio | {{ damping_ratio }} | - |14 15{% if archetype_description is defined %}16### Isolation Context17 18{{ archetype_description }}19{% endif %}20 21{% if tool_available %}22## Available Tool23 24A vibration transmissibility calculation tool is available at `/workspace/{{ meta.name }}_calc.py`. Run it with:25 26```bash27python3 /workspace/{{ meta.name }}_calc.py --help28```29 30You may use this tool to verify your calculations or compute values directly.31{% endif %}32 33## Required34 35Calculate the following:36 371. Frequency ratio382. Transmissibility393. Isolation efficiency in percent40 41## Constraints42 43- No internet access is available. Work from engineering knowledge and the provided tool.44- Use frequency ratio = forcing frequency / natural frequency.45- Use the damped force transmissibility equation provided by the tool.46- Use isolation efficiency = (1 - transmissibility) x 100.47 48## Output Format49 50Show your step-by-step working in Markdown. At the end of your solution, include a JSON block with your final answers in exactly this format:51 52```json53{54 "frequency_ratio": <numeric_value>,55 "transmissibility": <numeric_value>,56 "isolation_efficiency_pct": <numeric_value>57}58```59 60Write your complete solution to `/workspace/output.md`.61 62

Scenario archetypes

Each generated task is drawn from one of these realistic scenario bands.

Site contexts ground each scenario in a real locale the model can use to infer hidden values.

Pump isolator

pump_isolator

Pump or fan vibration isolator

plant-room-pumpfan-isolator
Parameter ranges
forcing_frequency_hz
20 – 80
natural_frequency_hz
2 – 15
damping_ratio
0.02 – 0.25

Precision equipment

precision_equipment

Precision equipment vibration isolation

laboratory-equipmentprecision-machine-base
Parameter ranges
forcing_frequency_hz
5 – 60
natural_frequency_hz
1 – 10
damping_ratio
0.02 – 0.35

Example task

laboratory-equipment-precision-equipment-preview — hard difficulty, all inputs given.

Precision equipment vibration isolation. laboratory-equipment. Required outputs: frequency_ratio, transmissibility, isolation_efficiency_pct

The model sees

Scenario context and visible inputs.

forcing_frequency_hz
5 to 60 Hz
natural_frequency_hz
1 to 10 Hz
damping_ratio
0.02 to 0.35 -

Executable tool: vibration-transmissibility_calc.py

The model must infer

Inputs withheld at this difficulty.

Nothing. All inputs are supplied.

The model must produce

The scored JSON answer schema.

{
  "frequency_ratio": <number>,
  "transmissibility": <number>,
  "isolation_efficiency_pct": <number>
}
  • frequency_ratio · scored within ±3%
  • transmissibility · scored within ±3%
  • isolation_efficiency_pct · scored within ±3%