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Consider a mass-spring system with mass m = 1, spring constant k = 2, and damping constant b = 2. Set up the equation of motion, and find the general solution y(t). Describe the long-time behavior as in problems 1-3. Is this overdamping, critical damping, or underdamping?

Consider a mass-spring system with mass m = 1, spring constant k = 2, and damping constant b = 2. Set up the equation of motion, and find the general solution y(t). Describe the long-time behavior as in problems 1-3. Is this overdamping, critical damping, or underdamping?

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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In Problems 1-3, find the general solution, and describe the long-term behavior of y(t): exponen- tial growth, exponential decay, simple oscillations, damped oscillations, or growing oscillations. Hint: if there are multiple terms in the solution, the qualitative behavior is determined by the largest term, i.e. the term that wins out for large t. 1. y"+y' 6y = 0. 2. y" 4y' + 4y = 0. 3. yy' + y = 0. 4. Consider a mass-spring system with mass m = 1, spring constant k = 2, and damping constant b = 2. Set up the equation of motion, and find the general solution y(t). Describe the long-time behavior as in problems 1-3. Is this overdamping, critical damping, or underdamping?
Transcribed Image Text:In Problems 1-3, find the general solution, and describe the long-term behavior of y(t): exponen- tial growth, exponential decay, simple oscillations, damped oscillations, or growing oscillations. Hint: if there are multiple terms in the solution, the qualitative behavior is determined by the largest term, i.e. the term that wins out for large t. 1. y"+y' 6y = 0. 2. y" 4y' + 4y = 0. 3. yy' + y = 0. 4. Consider a mass-spring system with mass m = 1, spring constant k = 2, and damping constant b = 2. Set up the equation of motion, and find the general solution y(t). Describe the long-time behavior as in problems 1-3. Is this overdamping, critical damping, or underdamping?
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