## gerryliyana 2 years ago Solve the semi-imfinite plate problem if the bottom edge of width 20 is held at T = 0o for 0 < x < 10, and T = 100o for 10< x<20. And the other sides are at 0o

1. gerryliyana

Solve the semi-imfinite plate problem if the bottom edge of width 20 is held at: $T = 0^{o} \rightarrow 0 < x < 10$$T = 100^{o} \rightarrow 10 < x < 20$ and the other sides are at $$\ 0^{o}$$

2. gerryliyana

|dw:1366518323249:dw| @oldrin.bataku hbu mate ??

3. gerryliyana

have idea ?? i'm little bit confused for $$\ 100^{o}$$ ---> 10 < x < 20..,

4. LolWolf

Is this similar to the Fourier heat problem?

5. mukushla

gerry this is the same problem except that boundary condition for bottom edge

6. mukushla

we had (note that 10 turens to 20)$T = \sum_{n=1}^{\infty} a_ne^{-\frac{n \pi}{20} y} \sin (\frac{n \pi}{20} x)$now for evaluating $$a_n$$ using fourier series$T = 0 \rightarrow 0 < x < 10 \\ T = 100 \rightarrow 10 < x < 20 \\ \ \ @ \ \ y=0$so$a_n=\frac{2}{20} (\int_{0}^{10} 0 \times \sin (\frac{n \pi}{20} x) \ \text{d}x+\int_{10}^{20} 100 \times \sin (\frac{n \pi}{20} x) \ \text{d}x)$$a_n=\frac{1}{10} \int_{10}^{20} 100 \times \sin (\frac{n \pi}{20} x) \ \text{d}x=...$makes sense?