Simple Pendulum Numerical Simulation

This GeoGebra worksheet demonstrates a simple pendulum by numerically solving its differential equation with NSolveODE. It illustrates core mathematical concepts: trigonometric functions (sin, cos) for converting the pendulum angle into Cartesian coordinates, the numerical solution of a second‑order ODE, and parametric equations xp = L·sinθ, yp = -L·cosθ that trace the bob’s path. Construction details include Length and Segment to draw the rod, sliders for length L, initial angle θ0, initial angular velocity ω0, and gravity g, a button to trigger numerical integration, and the use of NSolveODE to obtain ω(t) and θ(t). The resulting locus is a circular arc. The activity is suitable for high‑school or undergraduate courses in calculus, physics, or mathematics, allowing students to explore ODE solving, trigonometry, and parametric graphing.