Getting it into your agent
One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.
npx skills add hamzabellouch/agent-skills --skill coupled-oscillators-normal-modesgit clone --depth 1 https://github.com/hamzabellouch/agent-skillsWrote this? Show the measurements
A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.
[](https://agentmods.dev/skills/hamzabellouch/agent-skills/coupled-oscillators-normal-modes)<a href="https://agentmods.dev/skills/hamzabellouch/agent-skills/coupled-oscillators-normal-modes"><img src="https://agentmods.dev/badge/skills/hamzabellouch/agent-skills/coupled-oscillators-normal-modes/github.svg" alt="Measured on agentmods" height="20"></a>Or the 80×15 button, for a site that already has a row of RSS and ATOM ones. Only the verdict fits; the numbers stay here.
<a href="https://agentmods.dev/skills/hamzabellouch/agent-skills/coupled-oscillators-normal-modes"><img src="https://agentmods.dev/badge/skills/hamzabellouch/agent-skills/coupled-oscillators-normal-modes.svg" alt="Reviewed on agentmods" width="80" height="20"></a>What it costs to keep this loaded
Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.
| Model | Per session | Once invoked |
|---|---|---|
| Fable 5.1 | $0.00044 | $0.00334 |
| Opus 5.5 | $0.00018 | $0.00134 |
| Sonnet 5.5 | $0.00009 | $0.00067 |
| Haiku 4.5 | $0.00004 | $0.00033 |
Grade A, and why
coupled-oscillators-normal-modes scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured 7d ago.
A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.
Nothing flagged
None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.
What it actually says
Coupled Oscillators and Normal Modes
ID: mech.oscillations.coupled_normal_modes
Domain: Mechanics → Oscillations & Waves
Difficulty: 4/5
Prerequisites
- mech.oscillations.shm
- math.linear_algebra
Core Concepts
- normal modes
- eigenfrequencies
- coupling
- beats
- mode shapes
Key Equations
$$ M\ddot{\vec x} + K\vec x = 0 $$ $$ \det(K - \omega^2 M) = 0 $$
Methods
- Write equations of motion in matrix form
- Solve the eigenvalue problem
- Superpose modes with initial conditions
Typical Problem Types
- Two coupled pendulums
- Masses connected by springs
- Molecular vibrations
Common Pitfalls
- Assuming independent oscillators
- Forgetting to use both modes in the general solution
Related Skills
- mech.waves.standing
- qm.schrodinger.harmonic_oscillator
References
- Taylor Ch.11
- Goldstein Ch.6
What ships with it
1 file beside SKILL.md in the same directory: the scripts, references and assets a skill reads on demand. Not counted in the per-session cost; read them before you install if any of them is executable.
What this file has done since we first saw it
Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.
- 7d ago First seen · 57 lines · 44 tokens per session scan A ac5e15d27da4
coupled-oscillators-normal-modes is a skill published in the GitHub repository hamzabellouch/agent-skills (8 stars, last pushed today), licensed MIT. It adds 44 tokens to every session and 334 once invoked, about $0.0002 per session on Opus 5.5. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-10-10.
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