The heat is at the edges. For the first scenario the metal bar has an initial temperature distribution as follows: u(x,0)={25, x < 0.8 0, x > 0.8 Where u (x, t) is in degrees Celsius and x is given in meters and t in seconds. *25 sin (dt 1) Evaluate the integral an used to express u ( x, t) as a Fourier series. 1 I 0.8 Sdt to determine the Fourier coefficients that will be 2.4 Verify you did 1) correctly by plotting u(x,0)=E5, a, sin( on the domain 0x<2.4 Evaluate c using c=- and k= 0.95 cal gm = and p=0.092- cal O= 8.92 which are the physical po cm-s+C cm^3 gmc parameters for Copper.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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The heat is at the edges.
For the first scenario the metal bar has an initial temperature distribution as follows:
(25, x < 0.8
u(x,0)=
0, x > 0.8
Where u (x, t) is in degrees Celsius and x is given in meters and t in seconds.
1
1) Evaluate the integral an=
2.4 '0
0.8
S* 25 sin
)dt to determine the Fourier coefficients that will be
used to express u x, t) as a Fourier series.
nx.
Verify you did 1) correctly by plotting u(x,0)=E; an sin
on the domain 0 x<2.4
2.4
cal
cal
Evaluate c using c=- and k= 0.95
gm
O= 8.92
= and p=0.092-
gmc
which are the physical
po
cmss*C
ст^3
parameters for Copper.
Transcribed Image Text:The heat is at the edges. For the first scenario the metal bar has an initial temperature distribution as follows: (25, x < 0.8 u(x,0)= 0, x > 0.8 Where u (x, t) is in degrees Celsius and x is given in meters and t in seconds. 1 1) Evaluate the integral an= 2.4 '0 0.8 S* 25 sin )dt to determine the Fourier coefficients that will be used to express u x, t) as a Fourier series. nx. Verify you did 1) correctly by plotting u(x,0)=E; an sin on the domain 0 x<2.4 2.4 cal cal Evaluate c using c=- and k= 0.95 gm O= 8.92 = and p=0.092- gmc which are the physical po cmss*C ст^3 parameters for Copper.
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