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Unformatted text preview: ME147 Vibration and Control Systems Fall 2010 Wang 1-st Test 1. A mechanical system is shown in Fig. 1 .The disk can rotate about the point o. For analysis let the displacement variable x to be the response variable. 1-a. Derive the dynamic equation of motion for the given system. 1-b. If the damping coefficient c in the system can be tuned, then find the value c so the system has the dynamic ratio £ = 0.7. 1-c. For the system designed find the undamped, damped and resonant frequencies of this system. 1-d. If the initial conditions are given as x(0) = 0 and dx(0)7dt =0.5 m/sec, show the analytical form for x(t). * A - 4 2. Fig.2-a shows a experimental set-up for a torsional vibration study of a shaft with a disk. Note there is also a rotational damper in the system. When the disk is given an initial angular displacement of 9(0) = 8 degree ( = 0.14 rad) and d9 /dt = 0 at t = 0, and released from there, the response 9(t) of the disk is shown in Fig.2- b. The rod is 1.5 m long with a diameter d = 0.5 cm. The shear modulus of rigidity of the rod is G = 8 xlO 10 N/m 2 , the polar moment of inertia of the rod is...
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