A centrifugal pump, having an unbalance of \(m e\), is supported on a rigid foundation of mass \(m_{2}\) through isolator springs of stiffness \(k_{1}\), as shown in Fig. 5.54. If the soil stiffness and damping are \(k_{2}\) and \(c_{2}\), find the displacements of the pump and the foundation for the following data: \(m=0.25 \mathrm{~kg}, e=0.2 \mathrm{~m}, m_{1}=500 \mathrm{~kg}, k_{1}=500 \mathrm{kN} / \mathrm{m}, m_{2}=1000 \mathrm{~kg}\), \(k_{2}=250 \mathrm{kN} / \mathrm{m}, c_{2}=40 \mathrm{~N}-\mathrm{s} / \mathrm{m}\), and speed of pump \(=1200 \mathrm{rpm}\).

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8 8 8 8 000 hele 000 Centrifugal pump (mass, m) Isolator m k springs (stiffness, k) m Foundation (mass, m) FIGURE 5.54 Centrifugal pump. Soil (stiffness, k damping, c) 00000 k