Several previously published results have addressed the inverse eigenv
alue problem for lumped parameter non-conservative systems. These inve
rse results give conditions which allow the construction of mass norma
lized, velocity and position coefficient matrices based I on given eig
envalues and eigenvectors. Previous theories have examined the constru
ction of symmetric coefficients given complex and zero eigenvalues (ri
gid bodies). Here, the theory of real symmetric inverse eigenvalue pro
blems is extended to include the possibility of specifying real eigenv
alues, corresponding to overdamped modes. Specifically, conditions are
given that allow the construction of real, symmetric, mass normalized
damping and stiffness matrices given specified eigenvalues and eigenv
ectors, some of which may correspond to overdamped modes.