# Euler's helix and wave propagation in animated plot

I'm trying to create a complicated animated plot. The idea is to have a 3D helix, that is a projection of a point moving in a circle. Then the helix would de-convolute in a cosine and sine, similar to the following picture.

So far I can make a 3d helix but I don't know how to put everything together.

This is the code for the helix and this is what I get.

Animate[Module[{a},
Show[ParametricPlot3D[a = {Cos[t], Sin[t], t/4}, {t, 0, u},
ImageSize -> Small, PlotRange -> {{-2, 2}, {-2, 2}, {0, 8}}],
Graphics3D[{Red, Sphere[a, 0.15]}]]], {u, 10.^-6, 30},
AnimationRate -> 3]


Any idea on to do the animated plot?

You can combine multiple ParametricPlot3Ds. Here is something to begin with:

tRange = 5;
ω = 2;
offset = 1.2;

Animate[Show[
ParametricPlot3D[{t + δ, Cos[ω t + δ], Sin[ω t + δ]}, {t, -tRange, 0},
BoxRatios -> Automatic, PlotRange -> {{δ - tRange, δ + tRange},
{-offset - .1, offset + .1}, {-offset - .1, offset + .1}}, Boxed -> True,
Axes -> False, PlotStyle -> ColorData[97][3], Lighting -> "Neutral",
ViewProjection -> "Ortographic"],
ParametricPlot3D[{{t + δ, Cos[ω t + δ], -offset},
{t + δ, offset, Sin[ω t + δ]}},
{t, 0, 20}, PlotStyle -> {Darker@Blue, Darker@Red}],
ParametricPlot3D[{δ, Cos[ϕ], Sin[ϕ]}, {ϕ, 0, 2 Pi}, PlotStyle -> {Gray}],
Graphics3D[{Opacity[.9, White], Polygon[{{δ, -offset, -offset}, {δ,
offset, -offset}, {δ, offset, offset}, {δ, -offset, offset}}], Yellow,
Sphere[{δ, Cos[δ], Sin[δ]}, .12], Darker@Blue,
Line[{{δ, Cos[δ], Sin[δ]}, {δ, Cos[δ], -offset}}], Darker@Red,
Line[{{δ, Cos[δ], Sin[δ]}, {δ, offset, Sin[δ]}}]
}]], {δ, 10 Pi, 0}]


You can use FaceGrids -> {{0, 1, 0}, {0, 0, -1}} but this will show the grids across whole faces. You can use Boxed -> False, and then manually draw the box only on the left half.