3. Consider the initial value problemmu" + yu' + ku = 0u(0)= uo, u'(0) = vo.Assume that we are in the critically damped case where y? = 4km.(a)Show that if no matter the values of uo and vo, lim∞ u(t) =0.(b)u(T) = 0 for some given positive time T.Assume that uo > 0. Find a condition on vo so that

Given:- mu"+γu'+ku=0 u(0)=u(0), u'(0)= ν0

3. Consider the initial value problem Smu" + yu' + ku = 0 u(0) = uo, u'(0) = vo. Assume that we are in the critically damped case where 72 = 4km. (a) 0. Show that if no matter the values of uo and vo, lim→∞ u(t) Assume that uo > 0. Find a condition on vo so that (b) u(T) = 0 for some given positive time T. %3!

3. Consider the initial value problem Smu" + yu' + ku = 0 u(0) = uo, u'(0) = vo. Assume that we are in the critically damped case where 72 = 4km. (a) 0. Show that if no matter the values of uo and vo, lim→∞ u(t) Assume that uo > 0. Find a condition on vo so that (b) u(T) = 0 for some given positive time T. %3!

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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Question

3. Consider the initial value problem
mu" + yu' + ku = 0
u(0)
= uo, u'(0) = vo.
Assume that we are in the critically damped case where y? = 4km.
(a)
Show that if no matter the values of uo and vo, lim∞ u(t) =
0.
(b)
u(T) = 0 for some given positive time T.
Assume that uo > 0. Find a condition on vo so that

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