Dear Jochen,
NREL does not support another post-processor for the linearized matrices separate from the MATLAB-based MBC3 tool. You can likely get by using the free Octave tool instead of MATLAB.
I’m not following why you’d take the square root of the eigenvalues and look at the real part. For a simple linear mass-spring-damper (m-k-c) system, the complex eigenvalue pair (lambda) would be:
lambda_1,2 = -omega_nzeta +/- omega_nSQRT(1-zeta^2)*j
where,
omega_n = SQRT(k/m) = natural frequency in rad/s
zeta = c/(2momega_n) = damping ratio in fraction of critical
j = SQRT(-1) = imaginary number
So, the natural frequency (omega_n), damped frequency (omega_d), and damping ratio (zeta), can be calculated from the eigenvalues by:
omega_n = SQRT( Re(lambda_1)*Re(lambda_2) - Im(lambda_1)Im(lambda_2) )
omega_d = Im(lambda_1)
zeta = -( Re(lambda_1) + Re(lambda_2) ) / ( 2omega_n )
(which works for any value of zeta and generalizes to second-order systems with many degrees of freedom for complex pairs of eigenvalues).
Best regards,