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Unformatted text preview: NORTH CAROLINA STATE UNIVERSITY Department of Mechanical and Aerospace Engineering MAE 3151 Dynamics of Machines
Summer I, 2010 MIDTERM EXAMINATION (June 9, 2010) Name
Student ID
Problem
15
20
15
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INSTRUCTIONS: 1. This is a closed book exam. You are allowed to have 9113; help sheet of hand—written summary. 2. Explicitly state What you are solving for and how. Box your ﬁnal answers. Also, one word
answers are not acceptable. 3. Be neat and clear. Your exams must be stapled. Name Problem 1 (15 points) A helical spring of stiffness k is cut into two halves and a mass m is connected to the two halves.
The natural period of this system is 0.55ec. If an identical spring is cut so that one part is one
fourth and the other part threefourths of the original length, and the same mass is connected to the two parts, write out the equation of motion for both cases and determine the natural period of
the second system. I I
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Given the following mechanism with m = 4kg, 6 = 2m, 0 = SON/msec, k = 200N / m. 1. Derive its equation of motion in terms of rotation angle 0,
2. Determine the natural frequency and damping ratio of the mechanism, 3. For the initial condition 0(0) = 0.1md, 9(0) = —0.2rad/ sec, determine its solution. govt“: I, W100” Java) FED 6f 1*: 5M". Tb» My 96w“ 2/”, :: ox ‘ W£M&
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<3"— @ZO./Do/H4) {oz/r22“ Name Problem 3 (15 points) Consider the base excitation problem for the following conﬁguration. Support 1 x(t)
I C 1m) = Ysin W The base motion is a displacement transmitted through a dashdot or pure damping element. Derive its equation of motion, the steady—state motion, and the force transmitted to the support in steady
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