Press the button: the chosen mode is evolved without damping for 6 periods; the period measured from zero crossings is compared with 2 pi / w_n.

N equal masses m coupled by identical springs k and fixed at both ends obey, for small transverse motion, m u_j'' = k (u_(j+1) - 2 u_j + u_(j-1)) - c u_j'. The system has exactly N independent normal modes, shapes u_j ~ sin(j n pi / (N+1)), each oscillating at w_n = 2 sqrt(k/m) sin(n pi / (2 (N+1))). For small n this is nearly linear in n (a string: w = c_s q); near n = N the curve flattens, which is the lattice dispersion that a continuous string does not have.

Choose a mode number to excite one mode and watch a single energy bar; choose Pluck (mode 0) to displace only the middle mass and see energy spread over all odd modes (the even modes have a node there). Damping c drains every mode at rate c/(2m).

Simplifications: linear springs, small amplitudes, no tension change; the vertical scale is magnified so motion is visible. Integrator: velocity Verlet with step 0.05/w_max. Same system as the 3D page.