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Pendulum Wave Interference Simulation (2D)

Q: Is this the same physics as the 3D version?

Yes — both use theta_i(t) = theta_max times cos(2 pi t / T_i) with T_i = T / (N_base + i); this 2D view swaps the orbit-camera scene for a fixed side view so the wave shape reads clearly at a glance.

2D side-view pendulum-wave lab: a row of independent pendulums, each set to complete a different whole number of oscillations over one realignment period. Watch their individual sinusoidal motions superpose into a travelling wave that sweeps through standing-wave and scrambled-looking patterns, then snaps back into a straight line exactly on schedule.

Physics & Mechanics2DModerate60 FPS📱 Mobile-adapted⇄ 3D version

Each pendulum in this row starts at t = 0 with the same amplitude but a slightly different period, so pendulum i completes exactly N + i full swings during one realignment period — the same timing rule the 3D version uses. Their individually simple sinusoidal motions superpose into travelling-wave, standing-wave and seemingly chaotic shapes as the phases drift apart, then all recombine into a single flat line the instant the shared cycle completes, a direct visual proof of the superposition principle.

⚙ Under the hood

2D side-view pendulum-wave lab: N pendulums, each advancing at θ_max·cos(2π t / T_i) with T_i = T / (N_base + i), superpose into a travelling wave that sweeps through standing-wave and scrambled patterns before re-syncing exactly on schedule.

pendulum wavesuperpositioninterferencephase driftsimple harmonic motion

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install

Why do the pendulums keep re-syncing into a straight line?

Every pendulum shares the same starting phase at t = 0. Because pendulum i's period is exactly T_realign / (N_base + i), each one completes a whole number of oscillations in T_realign seconds — so after that time every pendulum is back at its own starting angle simultaneously, and the row looks flat again.

What determines the travelling-wave look?

Because neighbouring pendulums differ by exactly one extra oscillation over the cycle, their phase offset grows linearly along the row at any instant, which is the same condition that produces a travelling wave in a discretely sampled sinusoid.

Is this the same physics as the 3D version?

Yes — both use θ_i(t) = θ_max·cos(2π t / T_i) with T_i = T / (N_base + i); this 2D view swaps the orbit-camera scene for a fixed side view so the wave shape reads clearly at a glance.