A metal bar of length 1 = 1 and thermal diffusivity y = 1 is fully insulated, including itsends. Suppose the initial temperature distribution isu(0, x) =I{{0≤x≤1/2-1 1/2 ≤ 1≤1.(a) Use Fourier series to write down the temperature distribution at time t > 0.(b) What is the equilibrium temperature distribution in the bar, i.e., the limit of u(t, x)as t→∞o?

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A metal bar of length 1 = 1 and thermal diffusivity y = 1 is fully insulated, including its ends. Suppose the initial temperature distribution is u(0,r) = I {{ 0≤x≤1/2 - 1 1/2 ≤ 1 ≤ 1. (a) Use Fourier series to write down the temperature distribution at time t > 0. (b) What is the equilibrium temperature distribution in the bar, i.e., the limit of u(t, x) as t→∞o?

A metal bar of length 1 = 1 and thermal diffusivity y = 1 is fully insulated, including its ends. Suppose the initial temperature distribution is u(0,r) = I {{ 0≤x≤1/2 - 1 1/2 ≤ 1 ≤ 1. (a) Use Fourier series to write down the temperature distribution at time t > 0. (b) What is the equilibrium temperature distribution in the bar, i.e., the limit of u(t, x) as t→∞o?

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

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Buckling of columns

The column is described as a vertical member of the structure that carries an axial compressive load, and buckling is a lateral deformation of the column under the application of load.

Question

A metal bar of length 1 = 1 and thermal diffusivity y = 1 is fully insulated, including its
ends. Suppose the initial temperature distribution is
u(0, x) =
I
{{
0≤x≤1/2
-1 1/2 ≤ 1≤1.
(a) Use Fourier series to write down the temperature distribution at time t > 0.
(b) What is the equilibrium temperature distribution in the bar, i.e., the limit of u(t, x)
as t→∞o?

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