Watch coupled modes exchange their character
Sweep a shape parameter, weaken the coupling, and watch five computed eigenmodes approach and exchange their basis character. Follow a sorted mode index or highlight the contribution of one fixed basis shape.
Eigenvector character · squared basis weights
Set g to zero to recover uncoupled crossings, then raise it to open avoided gaps. In Basis character mode, bright segments measure squared overlap with one fixed basis vector. The highlighted eigenvalue can change index when that character moves between modes; near exact degeneracy a unique eigenvector is not defined. Eigenvalue λ is proportional to frequency squared, not frequency itself.
Model scope. A symmetric five-by-five operator retains the diagonal trends and nearest-neighbour coupling of the original teaching article. A live Jacobi eigensolve supplies eigenvalues and normalized eigenvectors. The animated shape uses five illustrative sine functions; it is not a native FEM geometry. Fixed-basis weights reveal character exchange, rather than implementing the native mesh-aware MAC tracker.