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[3] Consider the equation for free mechanical vibration, my" + by' + ky = 0 and assume the motion is critically damped. Let y(0) = Yo # 0 , and y'(0) = vo. Prove that the mass will pass through its equilibrium at one positive time if and only if 2myo 2mvo + byo Choose some specific m, b, k, yo to illustrate the result above by plotting the solutions (two examples Would suffice)

[3] Consider the equation for free mechanical vibration, my" + by' + ky = 0 and assume the motion is critically damped. Let y(0) = Yo # 0 , and y'(0) = vo. Prove that the mass will pass through its equilibrium at one positive time if and only if 2myo 2mvo + byo Choose some specific m, b, k, yo to illustrate the result above by plotting the solutions (two examples Would suffice)

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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[3] motion is critically damped. Let y(0) = yo 0, and y'(0) = vo. Prove that the mass will pass through its equilibrium at one positive time if and only if Consider the equation for free mechanical vibration, my" + by' + ky = 0 and assume the 2myo < 0 2тvo + byo Choose some specific m, b, k, Yo to illustrate the result above by plotting the solutions (two examples would suffice).
Transcribed Image Text:[3] motion is critically damped. Let y(0) = yo 0, and y'(0) = vo. Prove that the mass will pass through its equilibrium at one positive time if and only if Consider the equation for free mechanical vibration, my" + by' + ky = 0 and assume the 2myo < 0 2тvo + byo Choose some specific m, b, k, Yo to illustrate the result above by plotting the solutions (two examples would suffice).
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