plotting - Create a moving plot along a parametric plot using Manipulate?

I have been looking through Manipulate examples and haven't been able to create a working plot yet. I have a parametric plot defined:

Clear[f,x,y,t, surfaceplot]
{x[t_], y[t_]} = (t/2) {Cos[t], Sin[t]};
f[x_, y_] = 2 E^(-x^2 - y^2);
surfaceplot2 = Plot3D[f[x, y], {x, 0, 6Pi}, {y, 0, 6Pi}, AxesLabel -> {"x", "y", "z"}];

I am trying to create a point that moves along the plot from 0 to 6Pi using manipulate. I'm trying to adapt this code:

 Manipulate[ 
     ParametricPlot3D[ {x[t], y[t], f[x[t],y[t]]}, {t, 0, 6Pi}, 
         PerformanceGoal -> "Quality", 
         Epilog -> {Red, PointSize -> .05, Point[{x[t],y[t] }]}], 
     {{anotherT, 0}, 0, 6 Pi, Pi/64} ]

Does anyone have any thoughts on how to do this?

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