Plotting a Sum of Series

I have to plot these equations about the heat in a aluminium bar:

But for some reason, my graph of u(x,t)(in this case u on the code) is showing something different (i think the correct would be a exponential). Can someone review my code and see if is there any mistakes? Obs: n is the value where sin=0, for example sin(n*pi)=0 like in pi, 2pi, 3pi...

clc
clear all

syms x k t n

for n=1:1:20
cn=(100/(n*pi))*(cos(pi*x/4)-cos(3*pi*x/4));
    for t=0:5
    num=(cos(pi*x/4)-cos(3*pi*x/4));
    t1=exp((-(k^2)*(pi^2)*t)/1600);
    t2=sin(k*pi*x/40);
    S1=symsum((num*t1*t2),k,1,inf);
    u=((100/pi)*S1);
    end
end

fplot(cn)
figure
fplot(u)

[David Goodmanson]

Hi Italo,

One thing for sure, the integral in the top equation is incorrect. I believe it should be

(100/(n*pi))*( cos(n*pi/4) - cos(3*n*pi/4) )

and a sign of something wrong was that the c_n can't depend on x.

Could you state the actual problem, in particular the length of the bar?

Answer 1

[Roger Stafford]

You have forgotten to divide by k in calculating 'u' within your for-loop. You should have:

S1=symsum((num/k*t1*t2),k,1,inf);

[Ítalo Barros]

Tkx for the answer! But, even putting the 'k', the result is really strange:

Answer 2

[Vidya Bhadgaonkar]

I think you have one mistake in

t1=exp((-(k^2)*(pi^2)*t)/1600);

write it as

t1=exp((-(n^2)*(pi^2)*t)/1600);