Consider the Boundary-Initial Value problem Jºu 25 Ər² u(0, t) = 0, u(3,t) = 0, t>0 du u(x,0) = x(3 − x), Ət where b₂ - and C₂ J²u Ət² u(x, t) 0 0 This models the displacement u(x, t) of a freely vibrating string, with fixed ends, initial profile a: (3-2), and zero initial velocity. The solution z(x, t), is given by the series -(x,0)=0, 0

Consider the Boundary-Initial Value problem Jºu 25 Ər² u(0, t) = 0, u(3,t) = 0, t>0 du u(x,0) = x(3 − x), Ət where b₂ - and C₂ J²u Ət² u(x, t) 0 0 This models the displacement u(x, t) of a freely vibrating string, with fixed ends, initial profile a: (3-2), and zero initial velocity. The solution z(x, t), is given by the series -(x,0)=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

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Question

Transcribed Image Text:Consider the Boundary-Initial Value problem where b₂ and C₂ Jºu 25 Ər² u(0, t) = 0, u(3,t) = 0, t>0 du u(x,0) = x(3 − x), Ət J²u Ət² - This models the displacement u(x, t) of a freely vibrating string, with fixed ends, initial profile a: (3x), and zero initial velocity. The solution z(x, t), is given by the series 0<x<3, t> 0 u(x, t): -(x,0)=0, 0<x<3 n=1 b, sin (na) cos(c₂ t)

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