The base of a damped spring-mass system, with \(m=25 \mathrm{~kg}\) and \(k=2500 \mathrm{~N} / \mathrm{m}\), is subjected to a harmonic excitation \(y(t)=Y_{0} \cos \omega t\). The amplitude of the mass is found to be \(0.05 \mathrm{~m}\) when the base is excited at the natural frequency of the system with \(Y_{0}=0.01 \mathrm{~m}\). Determine the damping constant of the system.