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Four interactive physics models with equations, numerical exports, and original sources.
Standing wave simulator
A standing wave forms when waves travelling in opposite directions superpose. For an ideal string with fixed ends, allowed wavelengths are 2L/n and frequencies are nv/(2L). Nodes remain still while antinodes oscillate.
y(x,t) = A sin(nπx/L) cos(2πft)Open the experiment ↗INTERACTIVE MODELPendulum period simulator
For a simple pendulum at small angles, the period is approximately T = 2π√(L/g). Doubling the length increases the period by √2 rather than doubling it. At larger angles the small-angle formula becomes less accurate.
T ≈ 2π√(L/g)Open the experiment ↗INTERACTIVE MODELFrequency beats simulator
Two nearby frequencies superpose to create a changing amplitude envelope. The beat frequency is the absolute difference |f₁ − f₂|. A smaller frequency difference produces slower beats.
fbeat = |f₁ − f₂|Open the experiment ↗INTERACTIVE MODELLorenz attractor simulator
The Lorenz system is a set of three deterministic differential equations. Nearby initial conditions can diverge over time even when the parameters are identical. Its familiar two-lobed trajectory illustrates sensitivity to initial conditions.
ẋ = σ(y−x); ẏ = x(ρ−z)−y; ż = xy−βzOpen the experiment ↗Simulation exports are computed model data. Published human-study summaries are a separate collection.