2. Figure Q2 shows a 2DOF mass-elastic system model for studying the dynamics of a machine....

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2. Figure Q2 shows a 2DOF mass-elastic system model for studying the dynamics of a machine. This comprises two masses m and m2 which slide on frictionless surfaces connected by linear springs with stiffness values k, k2, and k3, and a single linear damper with coefficient c. Variables x, and X2 describe the absolute displacements of the mass m and m2. An external force f(t) is applied directly to m1. X2 XI k mi k2 k ww m2 f(t) D i) Figure Q2 Construct, via free-body diagrams and application of Newtonian mechanics, equations of motion for displacement variables X1, and x2, putting them into matrix form to identify the mass, damping, and stiffness matrices [M], [C], and [K], and excitation vector p(r). [10 marks] When individual mass-elastic parameter values are assigned m = 100 kg, m = 50 kg, k = 1010 N/m, k =510 N/m, and k =10x103 N/m, which results in a modal matrix [U] associated with E=[M]'[K] of magnitude: 0.7071 0.4472] [U]= -0.7071 0.8944 And with the inclusion of all sources of energy dissipation, damping matrix [C] is proportional to the mass matrix such that the magnitude of [C]=5[M]. 2. Figure Q2 shows a 2DOF mass-elastic system model for studying the dynamics of a machine. This comprises two masses m and m2 which slide on frictionless surfaces connected by linear springs with stiffness values k, k2, and k3, and a single linear damper with coefficient c. Variables x, and X2 describe the absolute displacements of the mass m and m2. An external force f(t) is applied directly to m1. X2 XI k mi k2 k ww m2 f(t) D i) Figure Q2 Construct, via free-body diagrams and application of Newtonian mechanics, equations of motion for displacement variables X1, and x2, putting them into matrix form to identify the mass, damping, and stiffness matrices [M], [C], and [K], and excitation vector p(r). [10 marks] When individual mass-elastic parameter values are assigned m = 100 kg, m = 50 kg, k = 1010 N/m, k =510 N/m, and k =10x103 N/m, which results in a modal matrix [U] associated with E=[M]'[K] of magnitude: 0.7071 0.4472] [U]= -0.7071 0.8944 And with the inclusion of all sources of energy dissipation, damping matrix [C] is proportional to the mass matrix such that the magnitude of [C]=5[M].