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Consider the Boundary-Initial Value problem where b = and C₁= 8²u 82² u(0,t)=0, u(4, t)=0, t>0 du u(a,0) = x(4-x), Ot 8²u 01²¹ 4 This models the displacement u(a, t) of a freely vibrating string, with fixed ends, initial profile z (4-2), and zero initial velocity. The solution u(x, t), is given by the series u(z, t) 00 = -(2,0)=0, 0

Consider the Boundary-Initial Value problem where b = and C₁= 8²u 82² u(0,t)=0, u(4, t)=0, t>0 du u(a,0) = x(4-x), Ot 8²u 01²¹ 4 This models the displacement u(a, t) of a freely vibrating string, with fixed ends, initial profile z (4-2), and zero initial velocity. The solution u(x, t), is given by the series u(z, t) 00 = -(2,0)=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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Consider the Boundary-Initial Value problem where b and C₁= 8²u 82² u(0,t)=0, u(4, t)=0, t>0 du u(a,0) = x(4-x), Ot 8²u 01²¹ 4 0<x<4, t>0 This models the displacement u(a, t) of a freely vibrating string, with fixed ends, initial profile z (4-2), and zero initial velocity. The solution u(x, t), is given by the series -(2,0)=0, 0<z < 4 u(z, t) ==b, n=1 b. sin (n=2) cos(c₂ t)
Transcribed Image Text:Consider the Boundary-Initial Value problem where b and C₁= 8²u 82² u(0,t)=0, u(4, t)=0, t>0 du u(a,0) = x(4-x), Ot 8²u 01²¹ 4 0<x<4, t>0 This models the displacement u(a, t) of a freely vibrating string, with fixed ends, initial profile z (4-2), and zero initial velocity. The solution u(x, t), is given by the series -(2,0)=0, 0<z < 4 u(z, t) ==b, n=1 b. sin (n=2) cos(c₂ t)
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