# homework5 - 6 Determine the natural period of vibration of...

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CE 222 ENGINEERING MECHANICS II ( FALL 2003 – 2004 ) EXERCISE SHEET V ( http://www.ce.metu.edu.tr/~ce222 ) 1. Determine the differential equation of motion of 10 kg block. The surface is smooth. The springs are originally unstretched. 2. The thin hoop of mass m is supported by a knife edge. Determine the natural period of vibration for small amplitudes of swing. 3. The disk, having a weight of 15 kN, is pinned at its center O and supports the block A that has a weight of 3 kN. If the belt which passes over the disk is not allowed to slip at its contacting surface, determine the natural period of vibration of the system. 4. If the slender rod has a weight of 5 N, determine the natural frequency of vibration. The springs are originally unstretched.

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5. The 6N weight is attached to the rods of negligible mass. Determine the natural frequency of vibration of the weight when it is displaced slightly from the equilibrium position and released.
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Unformatted text preview: 6. Determine the natural period of vibration of the disk having a mass m and radius r . Assume the disk does not slip on the surface of contact as it oscillates. 7. Determine the differential equation of motion of the 15 kg spool. Assume that it does not slip at the surface of contact as it oscillates. The radius of gyration of the spool about its center of mass is k G = 125mm. 8. If the block is subjected to the impressed force F =F .Cos ω t, show that the differential equation of motion is ( ) t Cos m F y m k y . . ω       = + & & where y is measured from the equilibrium position of the block. What is the general solution of this equation? 9. The 15 kg block is attached to two springs having a stiffness of 150 N/m. A force F=( 40.Cos 3t) N , where t is in seconds, is applied to the block. Determine the maximum speed of the block after frictional forces cause the free vibrations to dampen out....
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## This note was uploaded on 06/24/2009 for the course CE xxx taught by Professor Tuken during the Spring '09 term at Middle East Technical University.

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homework5 - 6 Determine the natural period of vibration of...

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