Summary

Mathematica 11.0 code

p1 = Table[
   Show[
    Plot[Cos[x] Sin[t], {x, 0, 9}, 
     PlotStyle -> {Gray, Thick, Opacity[(Erf[t - 6.5] + 1)/2]}, 
     PlotRange -> {-1.1, 1.1}, Axes -> False]
    ,
    Plot[Cos[(1 + (2 \[Pi])/a) (x)] Sin[t], {x, 0, 9}, 
     PlotStyle -> {Purple, Thick, Opacity[(Erf[t - 13] + 1)/2]}]
    ,
    Plot[Cos[(1 + 2 (2 \[Pi])/a) (x)] Sin[t], {x, 0, 9}, 
     PlotStyle -> {Orange, Thick, Opacity[(Erf[t - 18.5] + 1)/2]}]
    ,
    Graphics[{PointSize[0.03], Point[p[t] ]} ]
    , PlotPoints -> 100
    ]
   , {t, 0, 25, 0.1}];
ListAnimate[p1, 10]

Licensing

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