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) Suppose a spring with spring constant 9 N/m is horizontal and has one end attached to a wall and the other end attached to a 4 kg mass. Suppose that the friction of the mass with the floor (i.e., the damping constant) is 1 Ns/m. a. Set up a differential equation that describes this system. Let a to denote the displacement, in meters, of the mass from its equilibrium position, and give your answer in terms of x, a', a". Assume that positive displacement means the mass is farther from the wall than when the system is at equilibrium. 4X"+x'+9x=0 help (equations) b. Find the general solution to your differential equation from the previous part. Use c and c2 to denote arbitrary constants. Use t for independent variable to represent the time elapsed in seconds. Enter c as c1 and c2 as c2. Your answer should be an equation of the form x=c1e^(-0.5t)sin(1.39194t)+c2e^(-0.25t)cos(1.39194t) help (equations)

) Suppose a spring with spring constant 9 N/m is horizontal and has one end attached to a wall and the other end attached to a 4 kg mass. Suppose that the friction of the mass with the floor (i.e., the damping constant) is 1 Ns/m. a. Set up a differential equation that describes this system. Let a to denote the displacement, in meters, of the mass from its equilibrium position, and give your answer in terms of x, a', a". Assume that positive displacement means the mass is farther from the wall than when the system is at equilibrium. 4X"+x'+9x=0 help (equations) b. Find the general solution to your differential equation from the previous part. Use c and c2 to denote arbitrary constants. Use t for independent variable to represent the time elapsed in seconds. Enter c as c1 and c2 as c2. Your answer should be an equation of the form x=c1e^(-0.5t)sin(1.39194t)+c2e^(-0.25t)cos(1.39194t) help (equations)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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.) Suppose a spring with spring constant 9 N/m is horizontal and has one end attached to a wall and the other end attached to a 4 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 z to 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. 4x"+x'+9x=0 help (equations) b. Find the general solution to your differential equation from the previous part. Use c and c2 to denote arbitrary constants. Use t for independent variable to represent the time elapsed in seconds. Enter c as c1 and c2 as c2. Your answer should be an equation of the form I = ... x=c1e^(-0.5t)sin(1.39194t)+c2e^(-0.25t)cos(1.39194t) help (equations) c. Is this system under damped, over damped, or critically damped? under damped Enter a value for the damping constant that would make the system critically damped. N.s/m help (numbers) 12
Transcribed Image Text:.) Suppose a spring with spring constant 9 N/m is horizontal and has one end attached to a wall and the other end attached to a 4 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 z to 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. 4x"+x'+9x=0 help (equations) b. Find the general solution to your differential equation from the previous part. Use c and c2 to denote arbitrary constants. Use t for independent variable to represent the time elapsed in seconds. Enter c as c1 and c2 as c2. Your answer should be an equation of the form I = ... x=c1e^(-0.5t)sin(1.39194t)+c2e^(-0.25t)cos(1.39194t) help (equations) c. Is this system under damped, over damped, or critically damped? under damped Enter a value for the damping constant that would make the system critically damped. N.s/m help (numbers) 12
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