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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. 1. (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
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Read each problem carefully. There are three pages and three problems, each worth 10 points.
Total points: 30.
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motion given. There is damping from the air and from the contact materials, which is represented by the
effective linear viscous damping term in the differential equation. In a free-vibration test, the oscillation
decayed such that over twenty cycles, the amplitude reduced by a factor of 3.51. That is X0JX20 = 3.51. The period of each oscillation was ta = 2~rf3 seconds. Find the value of the damping coefficient, c, as
defined in the equation of motion. (You can use small ~ approximations in the calculations, but ~ is
not zero.) (2~— 4) inR2O + cR2O + ~t~,ngR6 =
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