Answer Happy

Figure Q4 shows a simplified vibration model for a machine of mass m mounted on a foundation which is modelled as a spring and damper system. The mass of the machine is 1500 (kg). The spring stiffness constant of the elastic foundation is k-60 (MN/m) and the damping coefficient c=4000 (N s/m). The machine has an unbalanced component rotating at a constant angular velocity w = 205 (rad/s), which has a vertical component of the centripetal force of 1,0) = 15 sin(ex) (N) acting on the machine. LUC k 2 Figure 24 Derive the equation of motion of the vibration system; (a) (b) Determine the natural frequency and damping ratio of the vibration system; (c) Derive the expression of the steady-state amplitude in terms of the natural frequency, damping ratio of the motion of the machine, and determine the steady-state amplitude of the vibration system; (d) Determine the amplitude of the vibration dynamic loads acting on the base of the machine.