Natural frequency by 'damp(sys)'

So when I use damp(sys) for a second order system, it returns two different natural frequencies instead of one. Say, for system tf(1,[1 7 10]), the poles are -2 and -5, natural frequency should be sqrt(10), while using damp(tf(1,[1 7 10])), the natural frequency returns 2 and 5. I'm really confused. Please advise, thanks :-)

Answer 1

[Rick Rosson]

   % Undamped natural frequency (radians per second):
   omega_0 = sqrt(10);

   % Attenuation coefficient (radians per second):
   alpha = 7/2;

   % Damping factor (dimensionless):
   zeta = alpha/omega_0;

   % Damped natural frequency (radians per second):
   omega_d = sqrt(alpha^2 - omega_0^2);

   % Pole location (complex s-plane):
   poles(1) = -alpha + omega_d;
   poles(2) = -alpha - omega_d;