5) The shown mechanical microdevice comprises two identical shuttle masses elastically supported by several beams. Propose...

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5) The shown mechanical microdevice comprises two identical shuttle masses elastically supported by several beams. Propose a lumped-parameter mass-spring system for the x-direction motion of this system and derive the mathematical model of the natural response using the energy method. Calculate the natural frequencies and the corresponding modes (unit-norm eigenvectors). The beams have identical rectangular cross-sections with a width (in-plane dimension) w = 10 m and thickness (dimension perpendicular to the plane) h = 1 m. Known also are m = 1.2 10-10 kg, = 200 m, l = 120 m, Young's modulus E = 150 GPa, and mass density t = 5600 kg/m. (25 marks) Anchors m m X Anchors h 5) The shown mechanical microdevice comprises two identical shuttle masses elastically supported by several beams. Propose a lumped-parameter mass-spring system for the x-direction motion of this system and derive the mathematical model of the natural response using the energy method. Calculate the natural frequencies and the corresponding modes (unit-norm eigenvectors). The beams have identical rectangular cross-sections with a width (in-plane dimension) w = 10 m and thickness (dimension perpendicular to the plane) h = 1 m. Known also are m = 1.2 10-10 kg, = 200 m, l = 120 m, Young's modulus E = 150 GPa, and mass density t = 5600 kg/m. (25 marks) Anchors m m X Anchors h