11. Consider nonzero solutions to the following second order differential equation 1"(t) + ya'(t) + w²r(t) = 0, (2) where 7,w are nonzero constants, and t > 0, represents the time. We can define the total energy of the system to be (3) For t> 0, under what conditions is the total energy always decreasing? (a) 7, w² > 0 (b) 7,w > 0 (c) 7> 0, w < 0 (d) w> 0,7 #0 (e) w < 0,7 #0

11. Consider nonzero solutions to the following second order differential equation 1"(t) + ya'(t) + w²r(t) = 0, (2) where 7,w are nonzero constants, and t > 0, represents the time. We can define the total energy of the system to be (3) For t> 0, under what conditions is the total energy always decreasing? (a) 7, w² > 0 (b) 7,w > 0 (c) 7> 0, w < 0 (d) w> 0,7 #0 (e) w < 0,7 #0

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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

11. Consider nonzero solutions to the following second order differential equation
z"(t) + ya'(t) + w?x(t) =
= 0,
(2)
where y,w are nonzero constants, and t > 0, represents the time. We can define the total energy
of the system to be
(3)
For t> 0, under what conditions is the total energy always decreasing?
(a) 7, w² > 0
(b) 7,w >0
(c) y> 0, w < 0
(d) w> 0,7 #0
(e) w< 0,70

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