This 2D companion replaces the 3D version's fixed multi-pendulum wave array with a single, fully adjustable simple pendulum, matching the "adjust mass and length, watch the period" premise the 3D page describes but never actually let you control. Every frame integrates the real equation of motion
theta''(t) = -(g / L) * sin(theta(t)) - c * theta'(t)
with RK4 sub-stepping (8 steps/frame), where c is the damping rate. Switching "Exact ODE" off replaces sin(theta) with theta itself — the small-angle idealization used to derive the classic period formula T₀ = 2π√(L/g).
- Length changes the period; mass does not — a genuine SHM result you can verify by comparing the measured period as you drag each slider independently.
- Release angle past ~40° makes the exact nonlinear period measurably longer than T₀ — push it toward 170° to watch the divergence grow large.
- Gravity lets you compare period on the Moon (1.6 m/s²) through Jupiter (24.8 m/s²) without changing the pendulum itself.
- Damping bleeds mechanical energy out of the system; watch the KE/PE split and total energy readouts shrink toward zero as swings decay.