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6. Let 8(t) be the Dirac-delta function. The position u(x, t) of a vibrating string which satisfies Up = 8(t – 1) + 8(t – 2), ) < x < L,t > t, Utt - u(0, t) = u(L, t) = 0, t > 0, u(x,0) = u,(x, 0) = 0, 0 < x < L. (a) Find the series solution. (b) Does the solution decay in time? Explain the physical interpretation of your result.

6. Let 8(t) be the Dirac-delta function. The position u(x, t) of a vibrating string which satisfies Up = 8(t – 1) + 8(t – 2), ) < x < L,t > t, Utt - u(0, t) = u(L, t) = 0, t > 0, u(x,0) = u,(x, 0) = 0, 0 < x < L. (a) Find the series solution. (b) Does the solution decay in time? Explain the physical interpretation of your result.

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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6. Let 8(t) be the Dirac-delta function. The position u(x, t) of a vibrating string which satisfies Utt – Urr = = 8(t – 1) + 8(t – 2), 0 < x < L,t > t, u(0, t) = u(L, t) = 0, t > 0, u(x, 0) = u,(x, 0) = 0, 0 < x < L. (a) Find the series solution. (b) Does the solution decay in time? Explain the physical interpretation of your result.
Transcribed Image Text:6. Let 8(t) be the Dirac-delta function. The position u(x, t) of a vibrating string which satisfies Utt – Urr = = 8(t – 1) + 8(t – 2), 0 < x < L,t > t, u(0, t) = u(L, t) = 0, t > 0, u(x, 0) = u,(x, 0) = 0, 0 < x < L. (a) Find the series solution. (b) Does the solution decay in time? Explain the physical interpretation of your result.
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