# Fenômeno de Ressonância - Visualização Interativa

Visualização interativa do fenômeno de ressonância em osciladores harmônicos dirigidos - explore curvas de resposta amplitude-frequência, relações de fase, efeitos de amortecimento e aplicações do mundo real

> Página canônica: https://elysiatools.com/pt/visualizations/resonance-phenomenon

- **Categoria:** Physics

## Visão geral

Interactive visualization of resonance phenomenon in driven harmonic oscillators demonstrating energy transfer efficiency at natural frequency. Features dual visualization panels: Spring-mass system animation showing periodic driving force F = F₀·cos(ωt) with real-time displacement response, and amplitude-frequency resonance curve showing characteristic bell-shaped peak. Physics equations: Natural frequency f₀ = (1/2π)√(k/m), Driving force F = F₀·cos(ωt), Amplitude response A(ω) = F₀/m / √((ω₀² - ω²)² + (γω)²), Phase difference φ = arctan(γω/(ω₀² - ω²)), Resonance condition ω = ωᵣ = √(ω₀² - γ²/2), Quality factor Q = ω₀/γ. Interactive parameter controls: Mass m (1-10 kg), Stiffness k (10-500 N/m), Damping coefficient γ (0.01-2), Force amplitude F₀ (1-50 N), Driving frequency f_drive (0.1-5 Hz). Real-time visualizations: (1) Spring-mass animation with oscillating mass, dynamic spring compression/extension, driving force vector arrow with direction and magnitude, equilibrium reference line, real-time displacement and force values. (2) Amplitude-frequency curve plotting A vs f with prominent resonance peak at f₀, current frequency marker showing operating point on curve, natural frequency f₀ vertical dashed line. (3) Phase diagram showing phase difference φ ranging from 0° (low frequency, force in phase with displacement) through 90° (at resonance, force in phase with velocity) to 180° (high frequency, force opposite to displacement). Quick presets: Off resonance (f << f₀, small amplitude), At resonance (f = f₀, maximum amplitude), Underdamped (low γ, sharp peak), Overdamped (high γ, broad suppressed peak), Frequency sweep (auto-scan f from 0.1 to 5 Hz to observe resonance traversal). Real-time statistics: Current amplitude, Max amplitude (at resonance), Resonance frequency fᵣ, Quality factor Q, Phase difference φ°. Educational content: Resonance conditions (f_drive = f₀, low damping, phase relationships), Damping effects on peak height and width (Q factor concept), Applications including swing pushing (pump at natural frequency for large amplitude), Bridge resonance (Tacoma Narrows 1940 collapse from wind-induced vortex shedding at f₀), Musical instruments (body resonance amplifies specific frequencies), MRI radio frequency (RF pulses at Larmor frequency resonate with hydrogen nuclei), Radio tuning (LC circuit resonance selects stations), Microwave ovens (2.45 GHz resonates with water molecules). Comparison scenarios: f_drive < f₀ (displacement lags force by 0-90°, small amplitude), f_drive = f₀ (90° phase lag, maximum amplitude, most efficient energy transfer), f_drive > f₀ (displacement lags by 90-180°, amplitude decreases). Frequency sweep demonstration showing how amplitude peaks dramatically when passing through resonance. Responsive design with synchronized canvas rendering. Multi-language support (zh, en, fr, de, es, pt, ru).

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