5. Figure 8 shows a damped spring-mass system that contains a pulley with radius R =0.2mand moment of inertia / =0.04kg.m , a mass m =1kg , one damping element withc= 2N. s/m, and two springs with force constant k, =3N/m and k, =6N/m. Both the twosprings remain unstretched, when m is in the position x=0. At time / =0, the mass m isreleased from rest in the position x=0, then it vibrates along the slope. Note that the cabledoes not slip relative to the pulley, and the air resistance against motion can be neglected.RmWkz30Figure 8.a) Draw the free-body diagrams of mass m and pulley I.(5 marks)b) Formulate the ordinary differentiation equation (ODE) of this vibration system.(5 marks)c) Find the equilibrium position, xe, of the mass.(3 marks)d) Determine the displacement of mass m as a function of time.(7 marks)
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