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Suppose a spring with spring constant 4 N/m is horizontal and has one end attached to a wall and the other end attached to a 3 kg mass. Suppose that the friction of the mass with the floor (i.e., the damping constant) is 1 N-s/m. a. Set up a differential equation that describes this system. Let a denote the displacement, in meters, of the mass from its equilibrium position, and give your answer in terms of x, x', x". Assume that positive displacement means the mass is farther from the wall than when the system is at equilibrium. help (equations) b. Find the general solution to your differential equation from the previous part. Use C1 and C2 to denote arbitrary constants. Use t for independent variable to represent the time elapsed in seconds. Enter c₁ as c1 and C2 as c2. Your answer should be an equation of the form x = .... help (equations).

Suppose a spring with spring constant 4 N/m is horizontal and has one end attached to a wall and the other end attached to a 3 kg mass. Suppose that the friction of the mass with the floor (i.e., the damping constant) is 1 N-s/m. a. Set up a differential equation that describes this system. Let a denote the displacement, in meters, of the mass from its equilibrium position, and give your answer in terms of x, x', x". Assume that positive displacement means the mass is farther from the wall than when the system is at equilibrium. help (equations) b. Find the general solution to your differential equation from the previous part. Use C1 and C2 to denote arbitrary constants. Use t for independent variable to represent the time elapsed in seconds. Enter c₁ as c1 and C2 as c2. Your answer should be an equation of the form x = .... help (equations).

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 18EQ
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Suppose a spring with spring constant 4 N/m is horizontal and has one end attached to a wall and the other end attached to a 3 kg mass. Suppose that the friction of the mass with the floor (i.e., the damping constant) is 1 N. s/m. a. Set up a differential equation that describes this system. Let x denote the displacement, in meters, of the mass from its equilibrium position, and give your answer in terms of a, a', a". Assume that positive displacement means the mass is farther from the wall than when the system is at equilibrium. help (equations) b. Find the general solution to your differential equation from the previous part. Use c₁ and c₂ to denote arbitrary constants. Use t for independent variable to represent the time elapsed in seconds. Enter c₁ as c1 and c2 as c2. Your answer should be an equation of the form a help (equations) c. Is this system under damped, over damped, or critically damped? 2. that would make the system critically damped. N s/m help (numbers) Enter a value for the damping constant
Transcribed Image Text:Suppose a spring with spring constant 4 N/m is horizontal and has one end attached to a wall and the other end attached to a 3 kg mass. Suppose that the friction of the mass with the floor (i.e., the damping constant) is 1 N. s/m. a. Set up a differential equation that describes this system. Let x denote the displacement, in meters, of the mass from its equilibrium position, and give your answer in terms of a, a', a". Assume that positive displacement means the mass is farther from the wall than when the system is at equilibrium. help (equations) b. Find the general solution to your differential equation from the previous part. Use c₁ and c₂ to denote arbitrary constants. Use t for independent variable to represent the time elapsed in seconds. Enter c₁ as c1 and c2 as c2. Your answer should be an equation of the form a help (equations) c. Is this system under damped, over damped, or critically damped? 2. that would make the system critically damped. N s/m help (numbers) Enter a value for the damping constant
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