Consider d?x = -kx ax3 Assume k > 0, m> 0, ¤ > 0, and o > 0. Show that as t → ∞, x → 0. [Hint: Form an energy integral and show dE/dt <0. Since E O (why ?), show that Fig. 26-9 implies that E - 0: E 26.9 Energy decay. Why can't E → E, > 0 as t → o ?]
Consider d?x = -kx ax3 Assume k > 0, m> 0, ¤ > 0, and o > 0. Show that as t → ∞, x → 0. [Hint: Form an energy integral and show dE/dt <0. Since E O (why ?), show that Fig. 26-9 implies that E - 0: E 26.9 Energy decay. Why can't E → E, > 0 as t → o ?]
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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![26.8. Consider
d?x
mdt?
-kx
ax3
Assume k > 0, m> 0, a > 0, and o > 0. Show that as t -- o, x -→ 0.
[Hint: Form an energy integral and show dE/dt <0. Since EZO (why ?),
show that Fig. 26-9 implies that E -- 0:
E
Figure 26.9 Energy decay.
Why can't E E, > 0 as t→ o ?]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffb1152d7-662d-4693-97cb-2c4f97d657e9%2Ff419fa74-1f1d-4293-b8ab-3bc5cabdf733%2Fyze75da_processed.png&w=3840&q=75)
Transcribed Image Text:26.8. Consider
d?x
mdt?
-kx
ax3
Assume k > 0, m> 0, a > 0, and o > 0. Show that as t -- o, x -→ 0.
[Hint: Form an energy integral and show dE/dt <0. Since EZO (why ?),
show that Fig. 26-9 implies that E -- 0:
E
Figure 26.9 Energy decay.
Why can't E E, > 0 as t→ o ?]
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