Driven massive field as a chain of coupled oscillators

This animation uses a finite chain with nearest-neighbor coupling, an on-site restoring term Ω²A, and a driven left boundary. The right edge includes an absorbing layer, which is better here than periodic boundaries because it prevents confusing wrap-around effects.

instantaneous profile A(x,t) running amplitude envelope driven left spring absorbing layer

Model

Interior sites obey

Ä = c² ΔA − Ω²A − γ(x)Ȧ

with a prescribed source at the left boundary.

Current regime: static

Controls

Motor amplitude A₀

Driving frequency ω

Field mass parameter Ω

Coupling c

Current values

t = 0.00

How to read it

ω = 0: static source. If Ω > 0, the static deformation is short-ranged; if Ω = 0, there is no mass-induced exponential screening and the static influence extends across the chain.

0 < ω < Ω: evanescent regime.

ω = Ω: idealized threshold mode. Here k = 0, so all oscillators are shown with the same phase and amplitude. The absorbing layer is disabled in this special pedagogical mode.

ω > Ω: propagating regime absorbed near the right boundary.