EngineerCore — Mechanical Engineering Calculator

Analyze Vibration

analyze_vibration

Read-onlyIdempotent

Analyse a mass-spring-damper system. Returns natural frequency (rad/s and Hz), damping ratio, damped natural frequency, system classification, logarithmic decrement, and engineering flags. All inputs must be in strict SI units.

Tool call template

Replace each placeholder with a value matching the input schema. Only required parameters are included; add optional parameters as needed.

{
  "id": 1,
  "jsonrpc": "2.0",
  "method": "tools/call",
  "params": {
    "arguments": {
      "mass": "<mass>",
      "stiffness": "<stiffness>",
      "damping_coefficient": "<damping_coefficient>"
    },
    "name": "analyze_vibration"
  }
}

Input Schema

Name	Required	Description
`mass`	Yes	Mass of the system in kilograms
`stiffness`	Yes	Spring stiffness in Newtons per metre
`damping_coefficient`	Yes	Damping coefficient in Newton-seconds per metre

Output Schema

Name	Required	Description
`f_d`	Yes	Damped natural frequency in Hz (underdamped only)
`f_n`	Yes	Natural frequency in Hertz
`zeta`	Yes	Damping ratio (dimensionless)
`omega_d`	Yes	Damped natural frequency in rad/s (underdamped only)
`omega_n`	Yes	Natural frequency in radians per second
`c_critical`	Yes	Critical damping coefficient in N·s/m
`log_decrement`	Yes	Logarithmic decrement (underdamped only)
`classification`	Yes	System damping classification
`engineering_flags`	Yes	Advisory messages about the system characteristics

Schema Changelog

Changes observed during successful MCP inspections.

First observedJul 24, 2026

TDQS

A4.2/5.0

Behavior4/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Annotations already declare readOnlyHint=true, idempotentHint=true, destructiveHint=false. The description adds that it returns outputs and requires SI units, providing useful context beyond annotations.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

Two sentences, front-loaded with purpose and outputs, no wasted words. Highly concise and structured.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness4/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Covers inputs, outputs, and constraints. Output schema exists (not shown here) which reduces burden. Could detail 'engineering flags' but overall complete.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters3/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema coverage is 100% with good descriptions. The description adds the overarching constraint of SI units but does not elaborate per-parameter beyond schema. Baseline 3 is appropriate.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly states the tool analyzes a mass-spring-damper system and lists specific outputs. It is distinct from siblings (analyze_state_space, tune_pid).

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines4/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

Explicitly states all inputs must be in strict SI units, which is a clear usage constraint. Implicitly indicates use for mass-spring-damper systems; lacks explicit when-not-to-use guidance but is adequate.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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