Standard Tier Module
Damped Oscillator
The closed-form damped harmonic oscillator, plotted and honestly labeled, in pure browser JavaScript.
See it run - a worked example, 100% in this browser tab
The problem
Engineers and students need a quick, trustworthy oscillator response without spinning up a numerical package or trusting an opaque online widget.
The local-first solution
This plugin evaluates the exact closed-form underdamped solution x(t) = A e^-gamma t cos(omega_d t) directly in the browser, with an auto-generated form and chart and no hidden network calls.
What it does
Closed-form x(t) for underdamped, critical, and overdamped regimes
Computes the damped frequency omega_d and oscillation period
Reports the 1/e decay time from the damping coefficient
Overlays the exponential envelope A e^-gamma t on the response
Auto-form with presets for underdamped and near-critical cases
Honest scope
Exact closed-form algebra in f64, validated against the analytic envelope and period. Because it routes no GeoNum drift, the trust pill is honestly marked untracked rather than reporting a fabricated verdict. It is an education and engineering tool, not certified design software.
Authorities cited
- Goldstein, Poole, Safko (2002). Classical Mechanics, 3rd ed., Ch. 3 - the damped harmonic oscillator.
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Plot an oscillator response
Generate the exact response in the browser and save it to Sandbox, attach it to a Worklog case, or route it into a Gate client portal. Nothing is uploaded to anyone's cloud.