One way to smooth things is to use an appropriate interpolating order: with random points. The ends can be flattened out with the Hamming Window.
points = Flatten[{HammingWindow[Range[-0.7, 0.7, 0.1]] RandomReal[{0, 1}, 10], 0}]; 15];
Plot[Interpolation[points, InterpolationOrder -> 5][t]3][t], {t, 1, 12Length[points]}]