Dear Kumara,
In my response to Arash, I was referring to the aerodynamic damping of the rotor, which results from a combination of blade, tower, and wind velocities. For most wind turbines operating normally, the aerodynamic damping from the rotor dominates over the aerodynamic damping from the tower, at least in the fore-aft direction (along the wind direction). But the aerodynamic damping of the rotor has a strong impact on the tower response.
Yes, your equation for the tower structural damping (c) is correct, except that FAST uses the equivalent expression in terms of stiffness, rather than mass:
c = 2zetastiffness/omega
Regarding this last point, see my post dated Oct 08, 2013 in the following topic for more information: Natural frequency and damping ratio calculation - #7 by Jason.Jonkman.
Best regards,