A motor of mass moment of inertia \(85 \mathrm{~kg} \cdot \mathrm{m}^{2}\) is attached to the end of the shaft of Chapter Problem 10.1. Determine the three lowest natural frequencies of the shaft and motor assembly. Compare the lowest natural frequency to that obtained by making a one-degree-of-freedom model and approximating the inertia effects of the shaft.

Data From Chapter Problem 10.1:

A \(5000 \mathrm{~N} \cdot \mathrm{m}\) torque is statically applied to the free end of a solid \(20-\mathrm{cm}\) radius steel shaft ( \(\left.G=80 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}, ho=7500 \mathrm{~kg} / \mathrm{m}^{3}\right)\) with a length of \(1.5 \mathrm{~m}\) that is fixed at one end and free at its other end. The torque is suddenly removed, and torsional oscillations begin.