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A mass of 4kg stretches a spring 40cm. Suppose the mass is displaced an additional 4cm in the positive (downward) direction and then released. Suppose that the damping constant is 2 N s/m and assume g = 9.8 m/s² is the gravitational acceleration. (a) Set up a differential equation that describes this system. Let to denote the displacement, in meters, of the mass from its equilibrium position, and give your answer in terms of I, I', I" (b) Enter the initial conditions: (0) = m I'(0) (c) Is this system under damped, over damped, or critically damped?? m/s

A mass of 4kg stretches a spring 40cm. Suppose the mass is displaced an additional 4cm in the positive (downward) direction and then released. Suppose that the damping constant is 2 N s/m and assume g = 9.8 m/s² is the gravitational acceleration. (a) Set up a differential equation that describes this system. Let to denote the displacement, in meters, of the mass from its equilibrium position, and give your answer in terms of I, I', I" (b) Enter the initial conditions: (0) = m I'(0) (c) Is this system under damped, over damped, or critically damped?? m/s

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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A mass of 4kg stretches a spring 40cm. Suppose the mass is displaced an additional 4cm in the positive (downward) direction and then released. Suppose that the damping constant is 2 N s/m and assume g = 9.8 m/s² is the gravitational acceleration. (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 1, x', " (b) Enter the initial conditions: (0) = m T'(0) (c) Is this system under damped, over damped, or critically damped?? m/s
Transcribed Image Text:A mass of 4kg stretches a spring 40cm. Suppose the mass is displaced an additional 4cm in the positive (downward) direction and then released. Suppose that the damping constant is 2 N s/m and assume g = 9.8 m/s² is the gravitational acceleration. (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 1, x', " (b) Enter the initial conditions: (0) = m T'(0) (c) Is this system under damped, over damped, or critically damped?? m/s
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