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 (153.97 KiB) Viewed 29 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, k,, of the four springs and the natural circular frequency of vibration, 0 (5 marks) (ii) The damping ratio, Ś, and hence identify the prevailing type of Damping. (b) For the ensuing vibration of the machine, (5 marks) (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) I Equilibrium position y = 100mm m w k Figure 6