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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
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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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.
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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2. Are there any points of the string, other than the ends, that do not move at all times? Explain.
Transcribed Image Text:2. Are there any points of the string, other than the ends, that do not move at all times? Explain.
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Follow-up Question
Are there any points of the string, other than the ends, that do not move at all times? Explain.
Transcribed Image Text:Are there any points of the string, other than the ends, that do not move at all times? Explain.
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