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Engineering · Mechanical Engineering
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A schematic of a dynamometer is shown in Figure V2. This mechanical system consists of a DC motor of mass moment of inertial Im and a break motor of inertia Ib connected by massless and 1 shafts of torsional stiffness k and k2 and a gear pair. The gears have radii rand r2 and inertia Igı T1 Figure V2: Schematic of Dynamometer Answer the following questions assuming that there is no slip between the gears and negligible damping between the gears. Derive the equations of motion of this torsional system in matrix form in terms of angular displacement. (50 points) Using im, 1b,Ig1,1g,-1 kg. m2, r1-2 and ki-k,-100 N. m/rad, find the natural frequencies and corresponding mode shapes. (40 points) Sketch the mode shapes on plot. (10 points) a. b. c.

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