CE573_Homework 10_2010 - CE 573 Structural Dynamics...

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1/2 CE 573 – Structural Dynamics Homework #10 due 12 November 2010, Friday, 1:30pm 1. Two objects of identical mass m are hanging from a ceiling with massless rigid rods of length L . The rods are connected to the ceiling with frictionless hinges. Furthermore, they are connected to each other at d distance from the hinges with a massless linear spring with stiffness k . When both rods are oriented vertically, the system is in equilibrium. Assume that oscillations are small and are about the vertical , i.e. small angles about the static equilibrium state. Note the presence of gravity . Hint: Write moment equilibrium equations about the frictionless hinges to derive the equations of motion. a. What is the minimum number of degrees of freedom required to describe this system? b. Write the differential equations of motion for the system. Make sure that you use small oscillations assumption to simplify (i.e., linearize) your derivation and answer. c.
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This note was uploaded on 02/03/2011 for the course CE 573 taught by Professor Various during the Spring '11 term at American University of Science & Tech.

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CE573_Homework 10_2010 - CE 573 Structural Dynamics...

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