anonymous 3 years ago 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

1. anonymous

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

2. anonymous

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

3. anonymous

ok.., i'll try :)

4. anonymous

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

5. anonymous

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 ??

6. anonymous

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

7. anonymous

@kropot72