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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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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