Pendulum Waves

i0 = 3; i1 = 9;
frame[t_] := Graphics[
   Table[
    {
     Opacity[0.9],
     With[{a = 0.3 + 0.1 (i - i0)/(i1 - i0)},
      With[{p = {Sin[a Cos[2 Pi i t]], -Cos[a Cos[2 Pi i t]] }/
          Sqrt[i], c = ColorData["DarkRainbow"][(i - i0)/(i1 - i0)]},
       {
        Darker@c,
        Line[{{0, 0}, p}],
        c,
        Disk[p, 0.008]}
       ]
      ]
     }
    , {i, i0, i1, 0.5}]
   , PlotRange -> {0.3 {-1, 1}, {-0.7, 0.05}}];
Manipulate[frame[t],{t,0,2}]