Pendulum — live

Mode

Physics is the rig's validated twin: α″ = −ωₙ²sinα − 2ζωₙα′ − c_d·α′|α′| + κF(pwm), with ωₙ=3.90 (T≈1.6 s), ζ=0.017, c_d=0.037, κF=0.00662·max(0,PWM−14.5), and a 0.20 s motor spin-up lag. The prop is push-only — the constraint that makes critical damping impossible and timing the key to pumping.