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CONCORDIA UNIVERSITY Faculty of Engineering and Computer Science ENGR 213 Applied Ordinary Differential Equations Winter 2015 Team Assignment No. 2 Page 1 of 3 Instructions: 1) Read Sections on 3.8.1, 3.8.2 and 3.8.3 (pages 150-159). 2) Form a team of two or three students to do the term assignment. A team must be formed to have all its two or three members belong to the same tutorial section. 3) You need to submit only one report per team. Your report must be well organized, logically presented and typed. Your report must have a cover sheet indicating clearly the names and student IDs of the team members, and your tutorial section. The report must include sufficient theoretical development of the dynamic model governing the mass-spring system in each of the problems given below. 4) The report must be submitted personally only in the tutorial class either on Friday, April 10, 2015 or on Monday, April 13, 2015 , depending on the tutorial section in which all the team members are enrolled in.
ENGR 213 Team Assignment No. 2 Winter 2015 Page 2 of 3 Problem 1. A 2-kg mass is attached to a spring with the spring constant ± ²³´µ¶· as shown in Figure P. 1. The mass is displaced by ¸¶¹´´· to the left of the equilibrium point and given a velocity of ¸´·¶º»¼ to the left. Neglecting the damping, determine the initial value-problem governing the motion of the mass. Solve the initial-value problem. What is the amplitude, period, and the natural frequency of the system? How long after the release does the mass pass for the first time through the equilibrium position? Figure P. 1 Problem 2. A 20-kg mass is attached to a spring with the spring constant 200 N/m as shown in Figure P. 2. The damping constant for the system is 140 N-sec/m. The mass is pulled 25 cm to the right of the equilibrium point and given an initial leftward velocity of 1 m/sec. develop and solve the mathematical model governing the motion of the mass. When will the mass return to its equilibrium position for the first time? Figure P. 2
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