= mg. Consider the mechanical system shown in Figure 3-46. Two pulleys, small and large, are...

  

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= mg. 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 k₁8 Assume that the displacement x 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 X wwwwww R, R₁ E wwwww www 8₂ Figure 3-46 Mechanical system. 105 = mg. 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 k₁8 Assume that the displacement x 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 X wwwwww R, R₁ E wwwww www 8₂ Figure 3-46 Mechanical system. 105