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Unformatted text preview: 2- 36Problems and Solutions Section 2.5(2.43 through 2.50)2.43A lathe can be modeled as an electric motor mounted on a steel table. The table plus themotor have a mass of 50 kg. The rotating parts of the lathe have a mass of 5 kg at adistance 0.1 m from the center. The damping ratio of the system is measured to be =0.06 (viscous damping) and its natural frequency is 7.5 Hz. Calculate the amplitude ofthe steady-state displacement of the motor, assuming r= 30 Hz.Soltuion:Given:m= 50 kg, 5=om, e= 0.1m, 06.=, n=7 5.HzLet r=30 HzSo, rrn==4From Equation 2.51,22222222)]4)(06.(2[)41(450)1.)(5()2()1(+=+=rrrmemXoX= 0.011mX = 1.1 cm2.44The system of Figure 2.15 produces a forced oscillation of varying frequency. As thefrequency is changed, it is noted that at resonance, the amplitude of the displacement is10 mm. As the frequency is increased several decades past resonance the amplitude ofthe displacement remains fixed at 1 mm. Estimate the damping ratio for the system.Solution: Equation 2.75 is2222)2()1(rrrmemXo+=At resonance, X= 10 mm = 21memo2110=emmoWhen ris very large, 1=emXmoand X= 1 mm, so1=emmoTherefore, 10(1) = 2105.=2- 372.45An electric motor (Figure P2.45) has an eccentric mass of 10 kg and is set on twoAn electric motor (Figure P2....
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- Spring '09