Oscillations & Waves

Simple & Large-Angle Nonlinear Pendulum Simulator

Test Galileo isochronism at small angles (sin θ ≈ θ) and measure period lengthening at large release amplitudes up to 170°.

Real-Time RK4 Kinematic / Dynamical Waveform Recorder

Physical Principles & Mathematical Derivation

θ̈ + (g / L) sin θ = 0, T₀ = 2π√(L / g)

Unlike textbook approximations that replace sin θ with θ, our RK4 solver integrates exact sin θ dynamics — letting you verify mass independence while observing true elliptic-integral period elongation above 30°!

Questions & Concepts

What physical equation governs Simple & Large-Angle Nonlinear Pendulum Simulator?

θ̈ + (g / L) sin θ = 0, T₀ = 2π√(L / g) — Unlike textbook approximations that replace sin θ with θ, our RK4 solver integrates exact sin θ dynamics — letting you verify mass independence while observing true elliptic-integral period elongation above 30°!

How are the equations of motion integrated in this simulation?

Nonlinear differential equations are integrated at 240–300 Hz substeps using classical 4th-order Runge-Kutta (RK4) to maintain strict Hamiltonian energy accuracy.

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