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ENGINEERING
8 (95%) A machine with a vibration absorber (aka tuned mann damper) can be maded as the two mass system shown in the figure, The equations of motion are given for each massas second order ordinary differential equations. Write your answers in terms of terms of m, m Au, en Note: The dampers are not shown in the figure but they are prenant in the system Equations of Motion mi T male () + kr(11 - 12) + kim = f maden - (11-12) - kz(11 - 12) = 0 (a) Decompose the 2 equations of motion into 4 first order differential equations. Show the substitutions and the resulting equations. These are the 4 state equations. (b) Write the system of 4 equations in state space form. Show the matrix form of the state equation (@) Write the output equation with output 1 as the displacement of mass 1, output 2 as the force in ki, and output 3 as the acceleration of the mass 2. Show the 3 individual output equations and the matrix form of the output equation.