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IBM

MCP Math Server

by IBM

pendulum_period

Calculate pendulum period and analyze pendulum motion using length, gravity, and angle inputs for trigonometric applications.

Instructions

Calculate pendulum period and analyze pendulum motion. (Domain: trigonometry, Category: applications)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
lengthYes
gravityNo
angleNo
Behavior2/5

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

No annotations are provided, so the description carries the full burden of behavioral disclosure. It states the tool calculates and analyzes, implying a read-only computation, but doesn't mention output format, error handling, assumptions (e.g., small-angle approximation), or performance characteristics. For a tool with three parameters and no annotations, this is a significant gap in transparency.

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

Conciseness4/5

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

The description is efficiently structured in a single sentence with a parenthetical note, making it easy to parse. It avoids redundancy and gets straight to the point, though the domain/category note could be more integrated. Every part serves a purpose, but it's slightly terse given the lack of parameter or usage details.

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

Completeness2/5

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

Given the tool's complexity (three parameters with physics implications), lack of annotations, and no output schema, the description is incomplete. It doesn't cover parameter semantics, behavioral traits, or return values, leaving critical gaps for an AI agent to use the tool correctly. The domain/category hint is helpful but insufficient for full contextual understanding.

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

Parameters2/5

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

The schema description coverage is 0%, meaning none of the three parameters (length, gravity, angle) are documented in the schema. The description adds no parameter-specific information—it doesn't explain units (e.g., meters for length, m/s² for gravity, radians/degrees for angle), default values (gravity has a default in schema but not mentioned), or constraints (e.g., angle range). With low coverage, the description fails to compensate, leaving parameters largely unexplained.

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

Purpose4/5

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

The description clearly states the tool's purpose with a specific verb ('Calculate') and resource ('pendulum period'), and adds 'analyze pendulum motion' for broader context. It distinguishes itself from siblings by specifying the domain (trigonometry) and category (applications), though it doesn't explicitly differentiate from other physics or motion-related tools in the list.

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

Usage Guidelines2/5

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

The description provides no guidance on when to use this tool versus alternatives. It mentions the domain and category but offers no explicit context, prerequisites, or comparisons to sibling tools (e.g., angular_velocity_from_period_or_frequency, oscillation_analysis, spring_oscillation), leaving the agent to infer usage based on parameter names alone.

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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