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Explain why it is necessary to conduct vibrational tests for structures Q5 (a) (5 marks) The block shown in Figure Q5 has a mass m and is supported on the solid ground by a spring with stiffness k and a parallel viscous damper with damping constant d. An out of balance force F(t) is exerted on the block. Suclh force F(t) is approximated by a harmonic function causing a steady state displacement x(t) shown in Figure Q5 The following relationship applies: Magnification Ratio M-) ) is the static deflection, η (2) is the where X,- frequency ratio of the forcing frequency to the undamped natural frequency and ζ is the damping ratio. Sketch the magnification ratio versus frequency ratio curves for the values of ζ-0, 0.25 and 1 superimposed on one another and showing the main points of the relations. (i) (5 marks) (i) With reference to your sketches highlight the possible advantages and disadvantages of the different levels of damping (5 marks) F(t) Fo sin (t) Mass, m x(t)X sin

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