Motion · phase portraits · differential equations

Pendulum Simulator

One motion, three perspectives. Watch the pendulum move through its phase plane and time history.

θ″ + (μ / mL) θ′ + (g / L) sin θ = 0

t = 0.00 s

Phase plane

Horizontal: θ (rad), unwrapped. Vertical: θ′ (rad/s). Filled green dots: downward equilibria. Hollow red dots: upright equilibria. Blue: solution curve; orange: current state.

Pendulum

Angle versus time

Computed with fourth-order Runge–Kutta. The physical display wraps naturally with each revolution; the plots preserve the full angle.