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Unformatted text preview: Home > My Assignments > Section 7.9 (Homework) About this Assignment SMALL BRIAN DIXON MA 241, section 009, Fall 2005 Instructor: Drew Pasteur North Carolina State University Due: Tuesday, November 1, 2005 11:07 PM EST Description Applications of Current Score: 7.25 out of 10.25 Second-Order Question Score Differential Equations pts subs 1 3/3 1/20 3/3 Viewing: Last Response View: All Responses Notes pts subs 1 3/3 1/20 3/3 Viewing: Last Response View: All Responses Notes pts subs 1 -/3 -/20 Notes pts 1 0.25/0.25 2 0.25/0.25 3 0.25/0.25 4 0.25/0.25 5 0.25/0.25 1.25/1.25 1. [SCalcCC2 7.9.02.] A spring with a 4 kg mass has natural length 1 m and is maintained stretched to a length of 1.3 m by a force of 24.3 N. If the spring is compressed to a length of 0.8 m and then released with zero velocity, find the position of the mass at any time t. x(t) = -.2*cos(4.5t) [-0.2*cos(4.5t)] 2. [SCalcCC2 7.9.04.] A spring with a 3 kg has damping constant 30 and spring constant 123. (a) Find the position of the mass at time t if it starts at the equilibrium position with a velocity of 2 m/s. x(t) = (1/2)exp(-5t)*sin(4*t) [(1/2)*exp(-5t)*sin(4t)] (b) Graph the position function of the mass. 3. [SCalcCC2 7.9.06.] A spring with a 5 kg has spring constant 123. Find the damping constant that would produce critical damping. (No Response)[49.6] subs 2/20 2/20 3/20 1/20 1/20 4. [SCalcCC2 7.9.08.] A spring has a mass of 1 kg and its damping constant is c = 10. The spring starts from its equilibrium position with a velocity of 1 m/s. Graph the position function for the following values of the spring constant k: 10, 20, 25, 30, 40. What type of damping occurs in each case? Viewing: Last Response View: All Responses Notes k = 10 k = 20 k = 25 k = 30 k = 40 overdamping overdamping critical damping underdamping underdamping [ overdamping ] [ overdamping ] [ critical damping ] [ underdamping ] [ underdamping ] Home My Assignments ...
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