A \(120-\mathrm{kg}\) fan with a rotating unbalance of \(0.35 \mathrm{~kg} \cdot \mathrm{m}\) is to be placed at the midspan of a \(2.6-\mathrm{m}\) simply supported beam. The beam is made of steel \(\left(E=210 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}\right.\) ) with a uniform rectangular cross section of height of \(5 \mathrm{~cm}\). For what values of the cross-sectional depth will the steady-state amplitude of the machine be limited to \(5 \mathrm{~mm}\) for all operating speeds between 50 and \(125 \mathrm{rad} / \mathrm{s}\) ?