Given that, u = cos(Act) sin(A. x) is an appropriate form of separated solution, solve the wave equation together with the conditions, Ә Ət u(0, t) = 0 u(π, t) = 0 u(x,0) = 0 u(x,0) = f(x), . t> 0, t> 0, 0 ≤ x ≤ π, and 0≤x≤n. for an arbitrary initial condition f(x) using the method of separated solutions. u(x, t) Your solution must contain a summation. Summations can be entered into the answer box in the form of sum(function, index variable, lower bound, upper bound). You must use index variable = n for your solution to be marked correctly. For example sum(A*B*C[n], n, 1, inf) = ₁ A.B. Cn Hint: we are dealing with the linear wave equation so we can superpose solutions. Check
Given that, u = cos(Act) sin(A. x) is an appropriate form of separated solution, solve the wave equation together with the conditions, Ә Ət u(0, t) = 0 u(π, t) = 0 u(x,0) = 0 u(x,0) = f(x), . t> 0, t> 0, 0 ≤ x ≤ π, and 0≤x≤n. for an arbitrary initial condition f(x) using the method of separated solutions. u(x, t) Your solution must contain a summation. Summations can be entered into the answer box in the form of sum(function, index variable, lower bound, upper bound). You must use index variable = n for your solution to be marked correctly. For example sum(A*B*C[n], n, 1, inf) = ₁ A.B. Cn Hint: we are dealing with the linear wave equation so we can superpose solutions. Check
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Given that, u = cos(Act)
sin(A. x) is an appropriate
form of separated solution, solve the wave equation together
with the conditions,
Ә
Ət
u(0, t) = 0
u(π, t) = 0
u(x,0) = 0
u(x,0) = f(x),
.
t> 0,
t> 0,
0 ≤ x ≤ π, and
0≤x≤n.
for an arbitrary initial condition f(x) using the method of
separated solutions.
u(x, t)
Your solution must contain a summation. Summations can be
entered into the answer box in the form of sum(function, index
variable, lower bound, upper bound). You must use index
variable = n for your solution to be marked correctly. For
example sum(A*B*C[n], n, 1, inf) = ₁ A.B. Cn
Hint: we are dealing with the linear wave equation so we can
superpose solutions.
Check](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fac4bd707-1db8-4976-9f6d-8edf92850988%2F49f87799-5785-47cd-8a8c-e775ef75f103%2Ffa7u99p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Given that, u = cos(Act)
sin(A. x) is an appropriate
form of separated solution, solve the wave equation together
with the conditions,
Ә
Ət
u(0, t) = 0
u(π, t) = 0
u(x,0) = 0
u(x,0) = f(x),
.
t> 0,
t> 0,
0 ≤ x ≤ π, and
0≤x≤n.
for an arbitrary initial condition f(x) using the method of
separated solutions.
u(x, t)
Your solution must contain a summation. Summations can be
entered into the answer box in the form of sum(function, index
variable, lower bound, upper bound). You must use index
variable = n for your solution to be marked correctly. For
example sum(A*B*C[n], n, 1, inf) = ₁ A.B. Cn
Hint: we are dealing with the linear wave equation so we can
superpose solutions.
Check
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