me445_hw6 - m 1 = m 2 /2 and k 1 = k 2 /2. Show that its...

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1 ME 445 Mechanical Vibrations // Fall 2009 Homework #6 Due: 28.12.2009 1. Determine the normal modes and frequencies of the system shown in Fig. P1, when n =1. Figure P1 2. For the system of Problem 1, determine the natural frequencies as a function of n . 3. Set up the matrix equation of motion for the system shown in Fig. P2 using coordinates x 1 and x 2 at m and 2 m . Determine the equation for the normal mode frequencies and describe the mode shapes. Figure P2 4. In Problem 3, Determine the matrix equation of motion if the coordinates x at m and θ are used. What form of coupling will result? 5. A two-story building is represented in Fig. P5 by a lumped mass system in which
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Unformatted text preview: m 1 = m 2 /2 and k 1 = k 2 /2. Show that its normal modes are Figure P5 6. In Problem 5, if a force is applied to m 1 to deflect it by unity and the system is released from this position, determine the equation of motion of each mass by the normal mode summation method. 7. Assume in Problem 5 that an earthquake causes the ground to oscillate in the horizontal direction according to the equation t X x g g ω sin = . Determine the response of the building and plot it against 1 . k k m 2m l l l m m k k nk x 1 x 2...
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This note was uploaded on 02/22/2010 for the course MECHANICAL ME 445 taught by Professor Namıkcıplak during the Fall '08 term at Yeditepe Üniversitesi.

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