A string with motionless ends at z = 0 and z = 1 vibrates according to the wave equation Fu Fu ət² 1. Use separation of variables (show details) to solve the equation provided that the initial profile of the string is u(x,0) = 4 sin(2x) and the initial velocity du Ət It=0 = 0.
A string with motionless ends at z = 0 and z = 1 vibrates according to the wave equation Fu Fu ət² 1. Use separation of variables (show details) to solve the equation provided that the initial profile of the string is u(x,0) = 4 sin(2x) and the initial velocity du Ət It=0 = 0.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![A string with motionless ends at x = 0 and x = 1 vibrates according to the
wave equation
Fu
Ət
and the initial velocity
5
1. Use separation of variables (show details) to solve the equation provided
that the initial profile of the string is
u(x,0) = 4 sin(2x)
?u
Ət
Ju
น
dr²
It=0
= 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F55521067-0384-497f-95f8-f51a06d5dbdf%2F4df4c6db-4903-43c7-ba10-01a80ca1c5c6%2Fe4fapn_processed.png&w=3840&q=75)
Transcribed Image Text:A string with motionless ends at x = 0 and x = 1 vibrates according to the
wave equation
Fu
Ət
and the initial velocity
5
1. Use separation of variables (show details) to solve the equation provided
that the initial profile of the string is
u(x,0) = 4 sin(2x)
?u
Ət
Ju
น
dr²
It=0
= 0.
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Follow-up Questions
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Follow-up Question
![2. Are there any points of the string, other than the ends, that do not move
at all times? Explain.](https://content.bartleby.com/qna-images/question/88ea2a71-9ac4-4e85-921f-8e0d04f36029/09c94c1e-a4dd-47e5-8bb3-3964257d8baf/xwkob5_thumbnail.png)
Transcribed Image Text:2. Are there any points of the string, other than the ends, that do not move
at all times? Explain.
Solution
Follow-up Question
![Are
there any points of the string, other than the ends, that do not move
at all times? Explain.](https://content.bartleby.com/qna-images/question/55521067-0384-497f-95f8-f51a06d5dbdf/6639efe0-a56c-444f-bed9-802b717e3da2/grcdc5l_thumbnail.png)
Transcribed Image Text:Are
there any points of the string, other than the ends, that do not move
at all times? Explain.
Solution
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