6. A machine of mass m = 2kg is supported by four springs and a damper of coefficient of damping c = 1 N.s/m, as shown i

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6 A Machine Of Mass M 2kg Is Supported By Four Springs And A Damper Of Coefficient Of Damping C 1 N S M As Shown I 1 (197.02 KiB) Viewed 39 times

6. A machine of mass m = 2kg is supported by four springs and a damper of coefficient of damping c = 1 N.s/m, as shown in Figure 6. It is observed that the equilibrium position is established after the springs have depressed by 24.5 mm under the weight of the machine. At time t=0, the machine is pushed down from its equilibrium position by y = 100mm , as shown, and then released. (a) For the system, (i) Calculate the total stiffness, kr, of the four springs and the natural circular frequency of vibration, an (5 marks) (ii) The damping ratio, 5 , and hence identify the prevailing type of Damping. (5 marks) (b) For the ensuing vibration of the machine, (i) Sketch the appropriate amplitude-time curve, and (6 marks) (ii) Determine the displacement of the machine from its equilibrium position after 5 oscillations. (9 marks) Total (25 marks) Equilibrium position y = 100mm m k k Figure 6