Answered: 3: Consider the One-Dimensional Wave… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.6: Additional Trigonometric Graphs

Problem 78E

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Question

3:
Consider the One-Dimensional Wave Equation for vibrations on a string
of length L with a free end and linear damping.
utt + but = c²UTT
u(t, 0) = 0 = u(t, L)
-
u(0, x) = f(x)
ut (0, x) = v(x)
Here, u(t, x) is the vertical displacement of the string, c is the wave speed,
and b is the coefficient of linear damping. Assume that
Пс
0<b<
L
so that all modes will be underdamped. Find a series representation for u
(including integral formulas for all the coefficients).

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