Question

Problem . Solve the semi-infinite plate problem if the bottom edge of width \(\ \pi\) is held at T=\(\\cos x \), and the other sides are at 0o

Answer 1

Solve the semi-infinite plate problem if the bottom edge of width \(\ \pi\) is held at T=\(\\cos x \), and the other sides are at 0o

Answer 2

this is the same problem gerryliyana, good practice for u :)

Answer 3

ok.., i'll try :)

Answer 4

the only thing has been changed is boundary condition of bottom edge and length of wall

Answer 5

Ok.., ok, i've tried. and i got
\[T (x,0) \sum_{n=1}^{\infty} a_{n} \sin (nx)\]
then into fourier form:
\[a_{n} \frac{ 2 }{ l } \int\limits_{0}^{l} f(x,0) \sin (nx) dx\]
because of T = f(x,0)= cos x for y =0; then
\[a_{n} = \frac{ 2 }{ \pi } \int\limits_{0}^{\pi} \cos x . \sin (nx) dx\]
how to solve \(a_{n} = \frac{ 2 }{ \pi } \int\limits_{0}^{\pi} \cos x . \sin (nx) dx\) ??
Would you kinly help me guys ??

Answer 6

@ajprincess @.Sam. @ganeshie8 @jim_thompson5910 would you kinly help me ??

Answer 7

@kropot72