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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 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, @, , (ii) The damping ratio, 5 , and hence identify the prevailing type of Damping. (b) For the ensuing vibratic of the machine, (i) Sketch the appropriate amplitude-time curve, and (ii) Determine the displacement of the machine from its equilibrium position after 5 oscillations. Equilibrium position y = 100mm k Figure 6

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, @, , (ii) The damping ratio, 5 , and hence identify the prevailing type of Damping. (b) For the ensuing vibratic of the machine, (i) Sketch the appropriate amplitude-time curve, and (ii) Determine the displacement of the machine from its equilibrium position after 5 oscillations. Equilibrium position y = 100mm k Figure 6

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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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 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, @, , (ii) The damping ratio, 5 , and hence identify the prevailing type of Damping. (b) For the ensuing vibration of the machine, (i) Sketch the appropriate amplitude-time curve, and (ii) Determine the displacement of the machine from its equilibrium position after 5 oscillations. Equilibrium position y = 100mm k C Figure 6
Transcribed Image Text: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, @, , (ii) The damping ratio, 5 , and hence identify the prevailing type of Damping. (b) For the ensuing vibration of the machine, (i) Sketch the appropriate amplitude-time curve, and (ii) Determine the displacement of the machine from its equilibrium position after 5 oscillations. Equilibrium position y = 100mm k C Figure 6
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