Concluding Remarks
The case of classical damping can be treated without the need for approximation.
When sufficient sensors are available one can extract m, c & k from the realization. In the general case, good estimates of flexibility at sensor points are available.
The non-classical case can be treated without approximation when the basis is complete.
For an incomplete basis and non-classical damping, approximations are needed because the damped and undamped modes don't span the same space.