To summarize this special case of model correction,
Is it not possible to replace a special pair,
Of experimentally determined natural frequencies?

Is this example a train consisting of four boxcars?
With no particular physical significance?
Or are the damping ratios, the analytical model data,
The shift in the complex conjugate eigenvalues,
Resulting in coefficient matricies, enough?

These are the natural frequencies of the undamped
System. Which decouples the equations of motion.
Note that the matrix produced, when corrected with rigid
Body modes, will have different damping ratios
Than those predicted by theory.