Assignment 3 _ANSWER

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Western University *

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3322

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Civil Engineering

Date

Apr 3, 2024

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4

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Western University Faculty of Engineering Department of Civil and Environmental Engineering CEE 3344b – Structural Dynamics I Assignment #3 Part A. (Solutions to Part A of each weekly assignment must be turned in by each student by the end of the tutorial period) Problem 1. A heavy table is supported by flat steel legs (Fig. 1). Its natural period in lateral virabtion is 0.5 sec. When a 50 lb plate is clamped to its surface, the natural period in lateral vibration is lengthened to 0.75 sec. What are the weight and the lateral stiffness of the table? Fig. 1 Answer:
Problem 2. Consider a diver weighing 200 lb at the end of a diving board that cantilevers out 3ft. The diver oscilates at a frequency of 2Hz. What is the flexural rigidity EI of the diving board? Answer:
Part B (Due 8:30am, on 5 th Feb., before the beginning of tutorial, submitted in person) Problem 1. The weight of the wooden block shown in Fig. 2 is 10 lb and the spring stiffness is 100 lb/in. A bullet weighing 0.5 lb is fired at a speed of 60ft/sec into the block and becomes embedded in the block. Determine the resulting motion u(t) of the block. Fig. 2
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Problem 2. Please derive the solution for the motion of a critically damped system due to initial displacement u(0) and initial velocity ˙ u ( 0 )

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