The motor-pump system shown in Fig. 5.36

(a) is modeled as a rigid bar of mass \(m=50 \mathrm{~kg}\) and mass moment of inertia \(J_{0}=100 \mathrm{~kg}-\mathrm{m}^{2}\). The foundation of the system can be replaced

by two springs of stiffness \(k_{1}=500 \mathrm{~N} / \mathrm{m}\) and \(k_{2}=200 \mathrm{~N} / \mathrm{m}\). Determine the natural frequencies of the system. Assume the distances between C.G. and springs ( \(k_{1}\) and \(\left.k_{2}\right)\) as \(l_{1}=0.4 \mathrm{~m}\) and \(l_{2}=0.6 \mathrm{~m}\).

Transcribed Image Text:

Motor 3 35 Pump T 0(t) x(t) C.G. x1(1) Base Foundation FIGURE 5.36 Motor-pump system on springs. 00000 (b) C.G. m, Jo k 00000 x2(1)