Problem 3. Let u(x, t) be the solution in [0, 1] × [0, +∞) of the problem 4uxx Utt = u|x=0 = ult=0 = 4 sin³ (πx), a)Find f(1/3), where u|x=1 = 0 ut t=0 = 30x(1x) f(t) = √" (u²(x, t) + 4u²(x, t)] da Hint: the integral has the meaning of the energy. What happens to the energy of a closed system? What is f'(t)? Could you prove your answer and use it to solve the problem? b)Find u(x, 2)
Problem 3. Let u(x, t) be the solution in [0, 1] × [0, +∞) of the problem 4uxx Utt = u|x=0 = ult=0 = 4 sin³ (πx), a)Find f(1/3), where u|x=1 = 0 ut t=0 = 30x(1x) f(t) = √" (u²(x, t) + 4u²(x, t)] da Hint: the integral has the meaning of the energy. What happens to the energy of a closed system? What is f'(t)? Could you prove your answer and use it to solve the problem? b)Find u(x, 2)
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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![Problem 3. Let u(x, t) be the solution in [0, 1] × [0, +∞) of the problem
4uxx
Utt =
u|x=0=u|x=1=0
ult=0 = 4 sin³ (7x), ut|t=0
a)Find f(1/3), where
=
30x(1-x)
ƒ(t) = [ * [u²(x, t) + 4u²(x, t)] da
Hint: the integral has the meaning of the energy. What happens to the energy of
a closed system? What is f'(t)? Could you prove your answer and use it to solve the
problem?
b)Find u(x, 2)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffb5fc8bb-c5ed-4c1c-8fd1-7dec9314987e%2F0d837411-a25c-498f-8189-82e18c3b8535%2F0vic18_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 3. Let u(x, t) be the solution in [0, 1] × [0, +∞) of the problem
4uxx
Utt =
u|x=0=u|x=1=0
ult=0 = 4 sin³ (7x), ut|t=0
a)Find f(1/3), where
=
30x(1-x)
ƒ(t) = [ * [u²(x, t) + 4u²(x, t)] da
Hint: the integral has the meaning of the energy. What happens to the energy of
a closed system? What is f'(t)? Could you prove your answer and use it to solve the
problem?
b)Find u(x, 2)
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