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EXAM 1, ME 461, February 22, 2012 Name Read each problem carefully. There are three pages and three problems, each worth 10 points. Include units in your answers, as appropriate. Total points: 30.
- (10 pts) The uniform bar of mass m and total length L = 4a, sketched below, rotates by an angle 0 (assumed small) about a frictionless pin at point 0, and lies in the horizontal plane. The mass M 2tn is considered to be a concentrated mass. Find the equation of motion in terms of 0 and the parameters a, k, c, and in. (Note that for a uniform slender bar of length L, the mass moment of inertia about its center of mass 0 is ‘G =±mL2)
Ic) ~Bar ~
In, 7-
1 4- (~J yfl~ØZ S f(tn~(3o;) 30~
1k
•1”I c4E~4+ G a —— 3 3
- (10 pts) The rigid bracket sketched below, with bar lengths L, is given an initial condition and its free vibration as measured. It is viscously damped. The equation of motion is also given for small angles 0. If in = 3 kg, k = 800 N/m, and xo/x2 = 1.87 is the ratio of the initial peak to the peak that occurs two cycles later, find the viscous damping coefficient, c. You can use small ~ approximations. C 4f~)flJt~f 20/5) - 3(gooW1~) k
a
L \JV~ (c~u c) ma~ê + ca2A + ka28 = 6 ~ ~Z~ 20 c/
IL/fl ~ S = C ,L-.~ 1, o~oc Sw~d~ I 3k +00 t-~ fl
tSwn
~vt. t, )k4~ 3
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