# RLC电路振荡 - RLC Circuit Oscillation

展示RLC电路阻尼振荡、谐振和能量转换的交互式模拟

> 标准页面: https://elysiatools.com/zh/visualizations/rlc-circuit-oscillation

- **分类:** Physics

## 概述

Interactive RLC circuit simulation demonstrating damped harmonic oscillations, resonance phenomena, and energy transfer between electric and magnetic fields. Features differential equation: Lq"" + Rq" + q/C = 0, natural frequency ω₀ = 1/√(LC), damping coefficient γ = R/(2L), damping ratio ζ = γ/ω₀, damped frequency ωd = √(ω₀² - γ²). Real-time visualization includes: (1) Waveform view showing charge Q(t) and current I(t) with exponential decay envelope; (2) Phase portrait (Q vs I) displaying spiral trajectory toward origin for damped systems; (3) Frequency response curve showing resonance peak at ω₀ with quality factor Q = ω₀L/R; (4) Energy transfer view showing continuous conversion between electric field energy (UE = q²/2C), magnetic field energy (UB = LI²/2), and heat dissipation (P = I²R); (5) Circuit diagram with R, L, C components and current flow. Adjustable parameters: resistance R (0-100 Ω), inductance L (0.1-10 H), capacitance C (0.1-5.0 F), initial charge Q₀ (1-20 C), animation speed (0.1-3.0x), time window (10-60 s), phase trail length (1-10), envelope scale (0.5-2.0x). Toggle display of charge and current curves independently. Five damping modes: underdamped (ζ < 1) with oscillatory decay, critically damped (ζ = 1) with fastest non-oscillatory return, overdamped (ζ > 1) with slow exponential decay. Educational content covers second-order differential equations, characteristic equation roots, relationship between circuit parameters and damping behavior, resonance condition and Q factor, energy conservation and dissipation, phase space analysis, and practical applications: tuning circuits (radio, TV), filters (audio, signal processing), oscillators and clock generators, voltage regulators, impedance matching, induction heating, wireless power transfer, and damping systems. Color coding: blue/cyan for charge Q, red for current I, green for energy, orange for dissipated heat. Multi-language support (zh, en, de, fr, es, ru, pt).

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