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Consider the mechanical system shown in Figure 3-46. Two pulleys, small and large, are bolted together and act as one piece. The total moment of inertia of the pulleys is J. The mass m is connected to the spring k, by a wire wrapped around the large pulley. The gravitational force mg causes static deflection of the spring such that k,& = mg. Assume that the displacement z of mass m is measured from the equilibrium position. Two springs (denoted by k) are connected by a wire that passes over the small pulley as shown in the figure. Each of the two springs is prestretched by an amount y. Obtain a mathematical model of the system. Also, obtain the natural frequency of the system. Problems 105

Consider the mechanical system shown in Figure 3-46. Two pulleys, small and large, are bolted together and act as one piece. The total moment of inertia of the pulleys is J. The mass m is connected to the spring k, by a wire wrapped around the large pulley. The gravitational force mg causes static deflection of the spring such that k,& = mg. Assume that the displacement z of mass m is measured from the equilibrium position. Two springs (denoted by k) are connected by a wire that passes over the small pulley as shown in the figure. Each of the two springs is prestretched by an amount y. Obtain a mathematical model of the system. Also, obtain the natural frequency of the system. Problems 105

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Use energy method Problem B-3-17 Consider the mechanical system shown in Figure 3-46. Two pulleys, small and large, are bolted together and act as one piece. The total moment of inertia of the pulleys is J. The mass m is connected to the spring k, by a wire wrapped around the large pulley. The gravitational force mg causes static deflection of the spring such that ki8 = mg. Assume that the displacement z of mass m is measured from the equilibrium position. Two springs (denoted by k2) are connected by a wire that passes over the small pulley as shown in the figure. Each of the two springs is prestretched by an amount y. Obtain a mathematical model of the system. Also, obtain the natural frequency of the system. Problems 105 Figure 6 Mechanical system. www wwww ww wwww
Transcribed Image Text:Use energy method Problem B-3-17 Consider the mechanical system shown in Figure 3-46. Two pulleys, small and large, are bolted together and act as one piece. The total moment of inertia of the pulleys is J. The mass m is connected to the spring k, by a wire wrapped around the large pulley. The gravitational force mg causes static deflection of the spring such that ki8 = mg. Assume that the displacement z of mass m is measured from the equilibrium position. Two springs (denoted by k2) are connected by a wire that passes over the small pulley as shown in the figure. Each of the two springs is prestretched by an amount y. Obtain a mathematical model of the system. Also, obtain the natural frequency of the system. Problems 105 Figure 6 Mechanical system. www wwww ww wwww
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