A spring-mass system with \(m=10 \mathrm{~kg}\) and \(k=5000 \mathrm{~N} / \mathrm{m}\) is subjected to a harmonic force of amplitude \(250 \mathrm{~N}\) and frequency \(\omega\). If the maximum amplitude of the mass is observed to be \(100 \mathrm{~mm}\), find the value of \(\omega\).