Physics
Explore physics principles through interactive simulations
103 visualizations
Damped Harmonic Oscillator - 弹簧振子
Interactive simulation of damped spring-mass-damper harmonic oscillator with real-time visualization of spring animation, displacement-time curve with exponential envelope, and phase space trajectory. Features equation of motion: mx'' + cx' + kx = 0, with solution x(t) = Ae^(-γt)cos(ωt+φ). Displays natural frequency ω₀ = √(k/m), damping ratio ζ = c/(2√(km)), and damped frequency ωd = ω₀√(1-ζ²). Three preset damping modes: underdamped (ζ < 1) with oscillatory decay, critically damped (ζ = 1) for fastest return without oscillation, and overdamped (ζ > 1) with slow non-oscillatory return. Adjustable parameters: spring constant k (5-100 N/m), mass m (0.5-5 kg), damping coefficient c (0-20 Ns/m), initial position x₀, and initial velocity v₀. Visual displays include real-time spring-mass animation with coil stretching, displacement vs time chart showing envelope decay, phase space plot (x vs v) with inward spiral trajectory, and energy vs time chart showing kinetic, potential, and total energy dissipation. Multi-language support (zh, en, es, fr, de, ru, pt).
Double Pendulum - 复摆混沌系统可视化
Explore chaotic motion in classical mechanics through an interactive double pendulum simulation. Features RK4 numerical integration for accurate energy conservation, real-time visualization of pendulum motion with velocity-colored trails (blue→red gradient), phase space plots (θ vs ω) showing chaotic attractors, and butterfly effect demonstration with 3 pendulums differing by 0.001 rad. Adjustable parameters: lengths l₁, l₂ (0.5-2.0 m), masses m₁, m₂ (0.5-5.0 kg), gravity g (1-20 m/s²), damping coefficient (0-0.5), and initial angles θ₁, θ₂ (-π to π). Preset configurations: horizontal (max potential energy), vertical (stable equilibrium), inverted (unstable equilibrium), and random. Real-time statistics display: time t, angles θ₁, θ₂, angular velocities ω₁, ω₂, kinetic energy T, potential energy V, and total energy E. Theory section includes Lagrangian mechanics derivation, equations of motion, chaos theory explanation, historical context (Lagrange 1788, Poincaré 1890s, Nature 2002), and observation guide. Demonstrates sensitive dependence on initial conditions, nonlinear coupling, and energy conservation. Perfect for physics education, chaos theory introduction, and classroom demonstrations. Multi-language support (zh, en, es, fr, de, ru, pt).
Communicating Vessels - 连通器原理
Interactive simulation of communicating vessels principle demonstrating pressure equilibrium and liquid level relationships. Features fundamental principle: same liquid at rest has equal levels (h₁ = h₂), pressure formula P = ρgh, and pressure balance at bottom. U-tube visualization with different tube diameters (left wide, right narrow) showing that diameter doesn't affect equilibrium height. Dual-liquid comparison: when different liquids (ρ₁ ≠ ρ₂) occupy sides, levels adjust according to pressure balance ρ₁gh₁ = ρ₂gh₂, giving level ratio h₁/h₂ = ρ₂/ρ₁ (denser liquid has lower level). Real-time visualization of liquid levels with color coding (blue: left liquid, red: right liquid), pressure markers at bottom showing equal pressure point P, and liquid level indicators h₁, h₂. Interactive comparison bar chart showing side-by-side height and density relationship. Adjustable parameters: left liquid density ρ₁ (500-2000 kg/m³) with presets (water 1000, oil 800, mercury 13600, alcohol 789, seawater 1260), right liquid density ρ₂, tilt angle θ (-30° to +30°), tube widths (left 30-100%, right 20-100%), and base liquid height. Display toggles for liquid levels, pressure points, force vectors, and grid. Preset scenarios: Same Liquid (ρ₁ = ρ₂, h₁ = h₂), Different Liquids (oil vs water showing level difference), and Tilted Vessel (demonstrating vertical height independence). Real-time calculations: left level h₁, right level h₂, level difference Δh, and bottom pressure P. Educational content covering communicating vessels principle, pressure equilibrium derivation, different liquid behavior, practical applications (water pots, tea kettles, boiler gauges, ship locks, construction levels), and tilting effects demonstrating that vertical height (not path length) determines pressure. Multi-language support (zh, en, fr, de, es, pt, ru).
Atmospheric Pressure vs Altitude - 大气压强随高度变化
Interactive visualization of atmospheric pressure variation with altitude using exponential decay model. Features fundamental barometric formula: P(h) = P₀·e^(-h/H) where P₀ = 101.325 kPa (sea level pressure), H = 8.5 km (scale height), and h is altitude. Density formula: ρ(h) = ρ₀·e^(-h/H) where ρ₀ = 1.225 kg/m³ (sea level air density). Earth and atmosphere cross-section visualization showing atmospheric layers (troposphere 0-12 km, stratosphere 12-20 km) with altitude scale 0-20 km and current altitude indicator. Real-time pressure gauge displaying current pressure reading with needle animation. Pressure vs altitude curve showing exponential decay with current operating point. Density vs altitude curve showing parallel exponential decay. Key altitude reference points: Sea Level (0 km, 101.3 kPa), Mt. Everest (8.85 km, 31.4 kPa), Airplane Cruise Altitude (11 km, 20.2 kPa), and Stratosphere (20 km, 5.5 kPa). Interactive controls: altitude slider (0-20 km), temperature adjustment (-50°C to 40°C) affecting scale height, atmospheric model parameters (scale height H, sea level pressure P₀, sea level density ρ₀), visualization toggles (pressure curve, density curve, key points, gauge), and animation mode for continuous ascent/descent. Quick presets: Sea Level, Mt. Everest, Airplane Cruise, Stratosphere, and Custom Parameters. Real-time displays: current altitude, pressure, density, and gauge needle position. Educational content covering exponential decay principles, scale height concept (pressure drops to 37% at 8.5 km), sea level standard atmosphere, half-pressure altitude (5.9 km), human physiological impact (hypoxia, acclimatization, death zone above 8000 m, aircraft pressurization), real-world applications (aviation, mountain climbing, weather forecasting, altitude training), model accuracy and limitations (ISA model, temperature variation, weather effects), and historical context (Torricelli's barometer 1643, Pascal's experiments 1648, International Standard Atmosphere 1950s). Multi-language support (zh, en, fr, de, es, pt, ru).
Sliding Friction - 滑动摩擦力
Interactive simulation of sliding friction with comprehensive static and kinetic friction analysis. Features physics formulas: static friction f_s ≤ μs·N (matches applied force until maximum), kinetic friction f_k = μk·N (constant when moving), normal force N = mg·cosθ, maximum static friction f_s,max = μs·N, and motion condition F > μs·mg·cosθ. Demonstrates stick-slip behavior with μs > μk relationship. Real-time visualization shows block on horizontal/inclined plane with force vectors (gravity mg: red downward, normal N: green perpendicular to surface, friction f: orange opposing motion, applied force F: purple in direction of push). Interactive f vs F graph showing three phases: static region (linear increase f = F), transition point (F = f_s,max), and kinetic region (constant f = f_k < f_s,max). Current operating point displayed with red dot on graph. Adjustable parameters: mass m (1-20 kg), static friction coefficient μs (0.1-1.0), kinetic friction coefficient μk (0.05-0.9), applied force F (0-100 N), gravity g (1.6-20 m/s²), and plane angle θ (0-45°). Real-time displays: friction force, normal force, applied force, state (static/kinetic), and motion indicator. Force display toggles for each vector. Educational content covering static friction principles, kinetic friction behavior, comparison of μs vs μk, stick-slip phenomenon, and real-world applications (brakes, tires, conveyor belts, mechanical systems). Multi-language support (zh, en, fr, de, es, pt, ru).
Longitudinal vs Transverse Waves - 纵波与横波对比
Interactive comparison of longitudinal and transverse waves with synchronized animation and particle motion visualization. Features fundamental wave equations: Transverse wave y(x,t) = A·sin(kx - ωt) where particles oscillate perpendicular to wave propagation direction creating crests and troughs; Longitudinal wave s(x,t) = A·sin(kx - ωt) where particles oscillate parallel to propagation creating compressions (密部) and rarefactions (疏部). Wave parameters: wavelength λ = v/f, wave number k = 2π/λ, angular frequency ω = 2πf, wave speed v = λ·f, period T = 1/f. Side-by-side synchronized animation with identical frequency and wavelength for direct comparison. Left panel shows transverse wave with vertical particle motion (sine wave pattern), right panel shows longitudinal wave with horizontal particle motion (compression-rarefaction pattern). Particle tracking with marked reference particle (red) showing oscillation path over time. Color-coded longitudinal particles: red for compression (high density), blue for rarefaction (low density). Particle trails showing oscillation history. Real-time wave properties display: wavelength, frequency, wave speed, and period. Waveform visualization overlay showing displacement curves. Comparison table highlighting key differences: particle motion direction, waveform shape, polarization capability, medium requirements, and real-world examples (transverse: electromagnetic waves, water waves; longitudinal: sound waves, pressure waves). Educational content covering wave classification, particle motion analysis, wave propagation principles, polarization concepts, and practical applications in acoustics, optics, and seismology (P-waves vs S-waves). Multi-language support (zh, en, es, fr, de, ru, pt).
Simple Machine Efficiency - 简单机械效率
Interactive simulation of simple machine efficiency comparing three fundamental machines: pulley systems, inclined planes, and levers. Features efficiency calculation η = (W_ideal / W_actual) × 100% = (F_ideal / F_actual) × 100%, where W_ideal = F_ideal·d (theoretical work without friction) and W_actual = F_actual·d (real work including energy losses). Physics formulas for each machine: Pulley system with mechanical advantage MA = 2n (n = number of pulleys), ideal force F_ideal = mg/(2n), actual force F_actual = F_ideal + μ·mg/n accounting for pulley friction. Inclined plane: ideal force F_ideal = mg·sin(θ), actual force F_actual = mg·sin(θ) + μ·mg·cos(θ) including friction, work ratio W_useful/W_total = sin(θ)/(sin(θ) + μ·cos(θ)). Lever: ideal mechanical advantage MA = L_effort/L_resistance, ideal force F_ideal = F_resistance/MA, actual force includes friction losses F_actual = F_ideal + μ·F_resistance. Three machine types with switchable interface, each with specific parameters (pulley count, load mass, friction; incline angle, length, mass; lever arm lengths, resistance force). Real-time force comparison bar chart showing ideal vs actual force. Work analysis diagram displaying energy flow from input to output with efficiency percentage. Energy flow chart breaking down total work into useful work (green) and friction losses (red). Machine efficiency comparison panel showing η values for all three types simultaneously. Dynamic parameter adjustment with instant efficiency recalculation. Educational content covering ideal vs real machines, friction effects, mechanical advantage concepts, energy conservation, practical applications in engineering and daily life. Multi-language support (zh, en, es, fr, de, ru, pt).
Conical Pendulum - 圆锥摆
Interactive simulation of conical pendulum motion with 3D visualization and comprehensive force analysis. Features circular motion in horizontal plane with constant angle θ to vertical. Physics formulas: centripetal force F_c = m·ω²·r = m·ω²·L·sin(θ), tension components T·cos(θ) = mg (vertical) and T·sin(θ) = m·ω²·L·sin(θ) (horizontal), period T = 2π√(L·cos(θ)/g), radius r = L·sin(θ), and velocity v = ω·r = ω·L·sin(θ). Three viewing modes: 3D perspective view showing conical motion, top view showing circular trajectory with velocity vector, and side view showing oscillatory projection. Real-time force diagram with tension T, gravity mg, and centripetal force F_c vectors. Motion charts: velocity vs time, centripetal force vs time. Energy analysis: constant kinetic energy (½mv²), potential energy (mgh), and total energy showing no energy exchange during motion. Comparison section highlighting differences from simple pendulum (circular vs oscillatory motion, constant vs varying angle, different period formulas, constant vs oscillating kinetic energy). Adjustable parameters: string length L, cone angle θ, angular velocity ω, gravity g, mass m, and trail length. Real-time displays: current angle, angular velocity, period, radius, time, tension, centripetal force, and energy values. Educational content covering force decomposition, circular motion principles, energy considerations, and applications in centrifugal governors and amusement rides. Multi-language support (zh, en, es, fr, de, ru, pt).
Simple Pendulum Motion - 单摆运动
Interactive simulation of simple pendulum motion with real-time visualization of angle θ, angular velocity ω, and energy conservation. Features the nonlinear equation θ'' + (g/L)sin(θ) = 0, small angle approximation θ'' + (g/L)θ = 0, period formula T = 2π√(L/g), and energy equation E = ½mL²θ'² + mgL(1-cosθ). Adjustable parameters: length L, initial angle θ₀, gravity g, mass m, and damping coefficient. Visual displays include real-time pendulum animation with trail, angle vs time chart, angular velocity vs time chart, and energy bar chart showing kinetic, potential, and total energy conservation. Multi-language support (zh, en, es, fr, de, ru, pt).
Semiconductor PN Junction - 半导体PN结
Interactive visualization of semiconductor PN junction physics - Explore P-type and N-type semiconductor junctions, energy band diagrams (conduction band, valence band, Fermi level), depletion region formation, built-in potential (V_bi = kT/e·ln(N_A·N_D/nᵢ²)), I-V characteristics (diode equation I = I₀(e^(eV/kT) - 1)), carrier concentration profiles, forward/reverse bias, avalanche and Zener breakdown, and real applications in diodes, LEDs, solar cells, and photodiodes with adjustable doping concentrations and temperature
Crystal Structures - 晶体结构
Interactive 3D crystal structure visualization - Explore cubic crystal systems (simple cubic, body-centered cubic, face-centered cubic), Bragg equation (2d·sinθ = nλ), Miller indices (hkl), d-spacing calculation (d_(hkl) = a/√(h²+k²+l²)), atomic density (ρ = n/V), coordination numbers, packing factors, X-ray diffraction patterns, and real-time interactive 3D models with adjustable lattice parameters
Osmotic Pressure Simulation - 渗透压模拟
Interactive visualization of osmotic pressure demonstrating van't Hoff equation (Π = iMRT), U-tube osmosis experiment with solvent flow dynamics, reverse osmosis with applied pressure, semipermeable membrane behavior, Π vs concentration relationship graphs, and real-world applications in biology, medicine, and water treatment with adjustable parameters for concentration, temperature, van't Hoff factor (i), and external pressure