In a multiple degree of freedom system (which a FEM system is) the number of natural frequencies and corresponding eigenvectors (= deformation modes) equals the number of degrees of freedom.
Now for the math: it is possible to re-state the mechanical problem in terms of eigen modes. If you do so you are left with a system of equations that is decoupled. This means that each eigenmode behaves like a single-mass spring system, with fictitious mass (m_i) and spring stiffness (k_i) corrrsonding to the equation sqrt(k_i/m_i) = omega_i, where omege_i is the natural frequency of vibration mode i.
What does this mean? Well that every natural frequency represents a physical singe mass-spring system corresponding to an eigenmode.
So in conclusion, natural frequencies for a multiple degree of freedom system (which a FEA system is) cannot be negative. In a rigid body motion you can at best only have 6 zero natural frequencies (corresponding to the 6 rigid body eigen modes. The rest should all be positive.
EDIT: instability may give rise to negative eigenvalues and (therefore) imaginary natural frequencies. This corresponds to exponential (rather than oscillatory) motion. See: https://forum.freecadweb.org/viewtopic. ... 30#p319635