The science
Lattice. Point masses m = ρa³ sit at the centres of cubic cells of edge a. Each edge carries a Hooke spring of stiffness k and each face diagonal one of k/2: F = k (L − L₀) For this lattice the continuum limit is C₁₁ = 2k/a, C₁₂ = C₄₄ = k/2a, hence E = 1.8 k / a, ν = 0.2 so the slider sets k = E a / 1.8.
Waves and wobble. A deformation travels at c = √(E/ρ). A column of height H, fixed at the bottom and free on top, rings at about f ≈ c / 4H = √(E/ρ) / 4H so quadrupling E doubles f. The exact lattice value (with Poisson coupling and discrete masses) is computed by inverse iteration on the stiffness matrix and shown next to the measurement.
Damping. Each spring has a dashpot c = βk. For a mode of angular frequency ω this gives the damping ratio ζ = β ω / 2, ω_d = ω √(1 − ζ²) and an amplitude that falls by e^(−2πζ/√(1−ζ²)) per cycle (logarithmic decrement). The dashpots are applied as exact exponential relaxation of the relative velocity, which is stable at any stiffness.
Integration. Symplectic Euler with dt = 1.4/ω_max (ω_max from the Gershgorin bound 2·max Σk / m) and many sub-steps per frame. The wobble sweep uses half that step.
Static sag. Under gravity a column compresses by about ρgH²/2E (a rod estimate); the sim measures the real value including lateral bulging and friction on the plate.
Simplifications. Linear springs (geometric nonlinearity only through large rotations), no volume-conservation term (ν fixed near 0.2), cubic anisotropy of the lattice (Zener ratio 0.67), contact with the plate by projection with Coulomb friction, ball contact by penalty springs. The shiny jelly surface is a Blender mesh bound to the lattice by trilinear free-form deformation.