2. Find the steady state in a square metal plate of side length a, if one side is held at a temperature T To and the remaining sides are held at T = 0. Treat this as a two-dimensional problem. In order to find the steady state solution, the time derivative in the heat equation can be set to zero. The result is the Laplace Equation, with no dependence on the thermal properties of the material. =
2. Find the steady state in a square metal plate of side length a, if one side is held at a temperature T To and the remaining sides are held at T = 0. Treat this as a two-dimensional problem. In order to find the steady state solution, the time derivative in the heat equation can be set to zero. The result is the Laplace Equation, with no dependence on the thermal properties of the material. =
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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How could I do Question 2.
![2. Find the steady state in a square metal plate of side length a, if one side is held
at a temperature T To and the remaining sides are held at T = 0. Treat this
as a two-dimensional problem. In order to find the steady state solution, the time
derivative in the heat equation can be set to zero. The result is the Laplace Equation,
with no dependence on the thermal properties of the material.
W
=
3. Using the basis functions un(x)=√√ sin , with n = 1,2,3,..., expand
nπx
ha
y(x) = {
-{-
(L-1)
L-a
f(x) =
x < a
x > a
over the interval [0, L]. This will be useful for a later homework problem involving a
plucked guitar string.
4. Be sure to read the hint at the bottom. For the function
1
(202)1/4 exp(-4³).
answer the following.
(a) Show that the normalization f(x) is such that f |ƒ(x)|² dx = 1.
defined by](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9b65ef36-cf51-4f81-80a6-74e205c9e9b1%2Ffc1c2d2b-12fa-488d-abab-c807f53d49bb%2Fqbwyystl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. Find the steady state in a square metal plate of side length a, if one side is held
at a temperature T To and the remaining sides are held at T = 0. Treat this
as a two-dimensional problem. In order to find the steady state solution, the time
derivative in the heat equation can be set to zero. The result is the Laplace Equation,
with no dependence on the thermal properties of the material.
W
=
3. Using the basis functions un(x)=√√ sin , with n = 1,2,3,..., expand
nπx
ha
y(x) = {
-{-
(L-1)
L-a
f(x) =
x < a
x > a
over the interval [0, L]. This will be useful for a later homework problem involving a
plucked guitar string.
4. Be sure to read the hint at the bottom. For the function
1
(202)1/4 exp(-4³).
answer the following.
(a) Show that the normalization f(x) is such that f |ƒ(x)|² dx = 1.
defined by
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