Consider the Boundary-Initial Value problem a²u J²u 9 მე2 Ət²' , 0 < x <5, t> 0 u(0,t) = 0, u(5,t) = 0, ди u(x, 0) = x(5 − x), at t>0 (x, 0) = 0, 0 < x < 5 This models the displacement u(x,t) of a freely vibrating string, with fixed ends, initial profile x (5 - x), and zero initial velocity. The solution u(x, t), is given by the series ∞ 4 u(x, t) = n=1 bɲ sin (· П (n = 7 x ) cos(cnt) where ཆུ་ང་ and Сп =
Consider the Boundary-Initial Value problem a²u J²u 9 მე2 Ət²' , 0 < x <5, t> 0 u(0,t) = 0, u(5,t) = 0, ди u(x, 0) = x(5 − x), at t>0 (x, 0) = 0, 0 < x < 5 This models the displacement u(x,t) of a freely vibrating string, with fixed ends, initial profile x (5 - x), and zero initial velocity. The solution u(x, t), is given by the series ∞ 4 u(x, t) = n=1 bɲ sin (· П (n = 7 x ) cos(cnt) where ཆུ་ང་ and Сп =
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 27E
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Question
![Consider the Boundary-Initial Value problem
a²u
J²u
9
მე2
Ət²'
,
0 < x <5, t> 0
u(0,t) = 0, u(5,t) = 0,
ди
u(x, 0) = x(5 − x),
at
t>0
(x, 0) = 0, 0 < x < 5
This models the displacement u(x,t) of a freely vibrating string, with fixed ends, initial profile x (5 - x), and zero initial velocity.
The solution u(x, t), is given by the series
∞
4
u(x, t)
=
n=1
bɲ sin (·
П
(n = 7 x ) cos(cnt)
where
ཆུ་ང་
and
Сп
=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7f867cd3-86ca-418d-9bd4-0389897a4f3d%2Fd852c55a-cf5d-4b3d-a782-05d57191d997%2Fnnb542_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the Boundary-Initial Value problem
a²u
J²u
9
მე2
Ət²'
,
0 < x <5, t> 0
u(0,t) = 0, u(5,t) = 0,
ди
u(x, 0) = x(5 − x),
at
t>0
(x, 0) = 0, 0 < x < 5
This models the displacement u(x,t) of a freely vibrating string, with fixed ends, initial profile x (5 - x), and zero initial velocity.
The solution u(x, t), is given by the series
∞
4
u(x, t)
=
n=1
bɲ sin (·
П
(n = 7 x ) cos(cnt)
where
ཆུ་ང་
and
Сп
=
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