Exercise problems

Q.1. A centrifugal pump rotating at 400 rpm is driven by an electric motor at 1200 rpm through a single stage reduction gearing. The moments of inertia of the pump impeller and the motor are 1500 kg.m² and 450 kg.m² respectively. The inertia of the gear and the pinion are 15 kg.m² and 5 kg.m² respectively. The lengths of the pump shaft and motor shaft are 500 and 200 mm, and their diameters are 100 and 50 mm respectively. Find the frequencies and the amplitudes of torsional vibration. G = 85 GN/m² .

Q.2. The system shown in figure below consists of two uniform rigid links of mass m and length L , a massless roller free to move in horizontally and two linear springs of stiffness k₁ and k₂, damper with damping coefficient c and a mass M.