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Homework2 - CEE511 Structural Dynamics Fall Semester...

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CEE511 – Structural Dynamics Fall Semester 2010-2011 Homework #2 (Due September 27, 2010) Modeling Discrete Parameter Systems - Equations of Motion 1. Chopra Problem 1.12 2. Chopra Problem 1.19 3. Derive the equations of motion for the following pendulum system. The rod length is L , and its mass density is uniform across its surface area. Assume b << L (so make small angle approximations). Mass density is but total mass of rod is m . Note: the term “rod” does not imply a simple rod. a. Derive the equation of motion of the system: b. Simplify the equation of motion assuming the displacement angle, , is small c. Determine the natural frequency of the rod system based on the simplified equation of motion in part (b). b L d. The same rod is taken and now rotated about a new pivot point (as shown below). Find the natural frequency of the new rod system configuration. Again, make small angle approximations to find the rod’s equation of motion.
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