A (50 mathrm{~kg}) pump is to be placed at the midspan of a (2.8-mathrm{m}) simply supported steel (left(E=200 times 10^{9} mathrm{~N} / mathrm{m}^{2} ight)) beam.

A \(50 \mathrm{~kg}\) pump is to be placed at the midspan of a \(2.8-\mathrm{m}\) simply supported steel \(\left(E=200 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}\right)\) beam. The beam is of rectangular cross section of width \(25 \mathrm{~cm}\). What are the allowable values of the cross-sectional height such that the natural frequency is outside the range of 50 to \(75 \mathrm{~Hz}\) ?