A water turbine of mass \(1000 \mathrm{~kg}\) and mass moment of inertia \(500 \mathrm{~kg}-\mathrm{m}^{2}\) is mounted on a steel shaft, as shown in Fig. 2.126. The operational speed of the turbine is \(2400 \mathrm{rpm}\). Assuming the ends of the shaft to be fixed, find the values of \(l, a\), and \(d\), such that the natural frequency of vibration of the turbine in each of the axial, transverse, and circumferential directions is greater than the operational speed of the turbine.

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d a FIGURE 2.126 Water turbine on a shaft.