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
Related questions
Question
![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)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
