Consider the three-mass system below. Assume the following: The heavy wheel m3 rolls against the vertical...

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Consider the three-mass system below. Assume the following: The heavy wheel m3 rolls against the vertical wall without slipping. The forces from springs k3 and k4 and the damper c2 pass through the center of the wheel and don't create any moments about the wheel. Small motions. No friction other than that required for RWS. Motions are deviations from SEP. Assume The pulley and cables are inextensible and massless. Derive the equations of motion for this system and arrange them in two different forms. Your answers will consist of the matrices described below and highlighted. 1. A general matrix form (that would be useful for vibrations analysis) and looks like: MX+Cx+ Kx = GF(t) In this equation M, C, K, and G are matrices (and the answers you need to submit). Use the vector x = [x 2. The standard state space form used in controls design: d - x = AX + Bu dt y = Cx In this equation A, B, and C are matrices (not the same as question 1). The input u is the force F(t) applied to mass 1, and x3 is the output. x= [X V x V x Vz] Consider the three-mass system below. Assume the following: The heavy wheel m3 rolls against the vertical wall without slipping. The forces from springs k3 and k4 and the damper c2 pass through the center of the wheel and don't create any moments about the wheel. Small motions. No friction other than that required for RWS. Motions are deviations from SEP. Assume The pulley and cables are inextensible and massless. Derive the equations of motion for this system and arrange them in two different forms. Your answers will consist of the matrices described below and highlighted. 1. A general matrix form (that would be useful for vibrations analysis) and looks like: MX+Cx+ Kx = GF(t) In this equation M, C, K, and G are matrices (and the answers you need to submit). Use the vector x = [x 2. The standard state space form used in controls design: d - x = AX + Bu dt y = Cx In this equation A, B, and C are matrices (not the same as question 1). The input u is the force F(t) applied to mass 1, and x3 is the output. x= [X V x V x Vz]

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We will first write down the equations of motion for each mass separately and then put them together ... View the full answer