Connect masses with elastic springs and the system finds its equilibrium while vibrating through normal modes. This is the mathematical backbone of cloth simulation, molecular dynamics, structural engineering and computer animation.
Each spring exerts a restoring force F = −k·Δx (Hooke's law). The equations of motion form a system of coupled ODEs integrated with Verlet. The eigenmodes of the stiffness matrix determine vibration frequencies — the same mathematics describes chemical bond vibrations and building resonance.
Drag any node to displace it and watch wave propagation. Add nodes with Click, connect them by dragging between two nodes. Adjust stiffness k and damping. Freeze one node to create a fixed boundary condition — observe standing waves.
The Tacoma Narrows Bridge collapsed in 1940 because its deck acted like a spring-mass system driven at its natural resonance frequency by 64 km/h winds. Modern suspension bridges include tuned mass dampers — heavy pendulums that absorb vibration energy.