Vibrating String with Damping

This analytical solution for a vibrating string was solved using the method of separation of variables assuming small linear perturbations. The rope was drawn using Mike Williams’ rope macro.

(* runtime: 2 seconds *)
c = 4; L = 1; h = 0.1; b = Pi; k := (n - 0.5)Pi/L; omega := Sqrt[(c k)^2 - (0.5b)^2];
Do[Plot[Evaluate[Sum[(6h/k^2)Sin[k/3] Exp[-0.5b t](Cos[omega t] + (0.5b/omega) Sin[omega t])Sin[k x], {n, 1, 10}]], {x, 0,L}, PlotRange -> {{0, L}, {-h, h}}, AspectRatio -> Automatic], {t, 0, 1.5, 0.025}];


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