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Homework3 - CEE511 Structural Dynamics Winter Semester...

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CEE511 – Structural Dynamics Winter Semester 2005-2006 Homework #3 (Due February 6, 2006) Single Degree of Freedom Systems – Free Vibration 1. Chopra Problem 2.6 2. Chopra Problem 2.20 3. Consider a heavy mass of weight W on the following beam system: EI = 10 6 k-in 2 massless beam W = 5 kips 60 in 60 in Assume the damping ratio of the beam is ξ = 10%. If displacement, u , corresponds to the displacement of beam at the location of the attached weight, and if the system is given an initial displacement of 0.5 in and an initial velocity of 15 in/sec determine the following: a. Write the equation of motion of the system – what type of system is it (i.e., underdamped, critically damped, overdamped)? b. The undamped natural frequency ( ω n ) and period ( T n ) of the system c. The damped natural frequency ( ω d ) and period ( T d ) of the system d. The critical damping coefficient, c cr e. Phase angle of the vibrating motion, θ f. The peak displacement at time t = T d + θ / ω d g. The peak displacement at time t = 2T d + θ / ω d h. The log-decrement, δ 4.
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