Consider a uniform rod of length L with an initial temperature given by u(x,0) = sin(Tx/L), 0 ≤x≤ L. Assume that both ends of the bar are insulated. (a) Find the temperature u(x, t). (b) What is the steady-state temperature as t→ ∞? (c) Let a² = 4 and L = 20. Plot u versus x for several values of t. Also plot u versus t for several values of x.
Consider a uniform rod of length L with an initial temperature given by u(x,0) = sin(Tx/L), 0 ≤x≤ L. Assume that both ends of the bar are insulated. (a) Find the temperature u(x, t). (b) What is the steady-state temperature as t→ ∞? (c) Let a² = 4 and L = 20. Plot u versus x for several values of t. Also plot u versus t for several values of x.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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![5. Consider a uniform rod of length L with an initial temperature given
by u(x,0)= sin(7x/L), 0 ≤ x ≤ L. Assume that both ends of the bar
are insulated.
(a) Find the temperature u(x, t).
(b) What is the steady-state temperature as t→ ∞?
(c) Let a²
4 and L = 20. Plot u versus x for several values of t.
Also plot u versus t for several values of x.
=
(d) Describe briefly how the temperature in the rod changes as time
progresses.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1720cd77-2294-45a6-8b70-43447dc02920%2F7755a9a6-6f81-43a4-9474-90df24c496f5%2F301mjo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:5. Consider a uniform rod of length L with an initial temperature given
by u(x,0)= sin(7x/L), 0 ≤ x ≤ L. Assume that both ends of the bar
are insulated.
(a) Find the temperature u(x, t).
(b) What is the steady-state temperature as t→ ∞?
(c) Let a²
4 and L = 20. Plot u versus x for several values of t.
Also plot u versus t for several values of x.
=
(d) Describe briefly how the temperature in the rod changes as time
progresses.
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