Tool
Driven damped pendulum
d²θ/dt² + γ dθ/dt + sin θ = A cos(ω t). The textbook 1-pendulum chaotic system. Scrub γ, A, ω to walk through the period-doubling cascade.
Pendulum
Phase portrait (θ, dθ/dt)
Driven, damped pendulum
d²θ/dt² + γ dθ/dt + sin θ = A cos(ω t)
A = 0: pendulum gradually settles to the rest state θ = 0.
A small, ω near 1: small linear oscillations.
A larger (≈ 1.0–1.5), γ ≈ 0.5: period-doubling cascade to chaos
(rotations + librations).FAQ