Here is the animatation for the vibrating string (without damping). I have rewitten the Cn's as in class.

> with(plots):

> m:=20: a:=1:

> animate({sum((-1)^(k+1)*8/((2*k-1)^2*Pi^2)*sin((2*k-1)*Pi*x/2)*cos((2*k-1)*Pi*a*t/2),
k=1..m)},x=0..2,t=0..10,frames=100,color=blue);

>