I · State-Space Rotation
X(t) = (x, v/ω) rotates uniformly; a = −ω²x restores
θ = 0.00
x = 0.00
v/ω = 0.00
a = 0.00
II · From Phase to Waves
Traveling wave (top) · Standing wave (bottom)
III · Coupled Oscillator Chain → Continuum Limit
Discrete masses with neighbor coupling; drag slider to increase N toward the wave equation