engineering.second_order_response

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

Goes well beyond the readOnly/idempotent annotations by disclosing output conventions that would otherwise be guesswork: overshoot is a 0–1 ratio (not percent), equals 0 for ζ≥1 and 1 for ζ=0, and settling_time is the 2% approximation 4/(ζωn) returning the literal string "Infinity" at ζ=0. Precision behavior (30 significant digits for transcendental functions) is also stated.

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

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

Dense but front-loaded — the formula and computed quantities come first, then input formats, then output conventions. Every sentence carries information; the only cost is that the terse run-on style makes the param-format clause easy to skim past.

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

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

Output schema exists so return values needn't be described, and the description still covers input format, edge cases, and precision — enough to call correctly. What is missing is any note on the boundary cases ζ=1 classification between regimes or on sibling selection, though neither blocks a correct call.

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

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

Schema description coverage is 0%, so the description must carry the load and largely does: it names ζ with the constraint '0 이상' and ωn with units rad/s and '>0', plus the Decimal-string format for both. Minor gap: it never explicitly re-uses the exact parameter names damping_ratio/natural_freq, relying on symbol mapping.

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

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

States the exact transfer function G(s)=ωn²/(s²+2ζωn·s+ωn²) and enumerates the outputs (ωd, peak overshoot, settling time, regime), which pins the tool down precisely and separates it from engineering.first_order_response without needing the schema.

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

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

Input validity ranges (ζ≥0, ωn>0 rad/s) imply when the tool is applicable, but there is no explicit 'use this instead of X' guidance and no named alternative. The agent must infer that first_order_response or bode_magnitude_phase are different tools.

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