Space Elevator Tether Modal Resonance (2D)

This 2D companion to the space-elevator tether-resonance simulator solves the exact same variable-tension wave equation as the 3D engine, but with an independent numerical method: instead of stepping every node forward in time, it diagonalizes the tether's discretized stiffness operator into true natural vibration modes and natural frequencies (a symmetric eigenvalue problem, solved with a Jacobi rotation algorithm), then represents the tether's motion as a sum of independent damped oscillators — one per mode — each driven by how strongly the climbing vehicle's current position overlaps that mode's shape. A live bar chart shows the amplitude of the lowest fifteen modes so you can see directly which vibration mode is absorbing the climber's forcing, and watch a real resonance emerge as the forcing frequency sweeps past a natural frequency — around 60x more steady-state sway at exact resonance than off it, verified numerically against the 3D engine's own finite-difference formulation.