Actually if you don't need an exact sine function you could do also using simple ramp for the sine with 3 entry black, white, black and set interpolation to smooth.

On the 2d placement, set V...

I don't think "time" is appropriate in this case, as you said your object will be displaced with same amount of value in time, you won't get wave kind displacement.

I got an idea.

Basically I'm...

When you duplicate a model that has been skinned (ummm, that word seems a bit awful), all transform are locked (greyed out in channel box).

Since it is locked you can't move the duplicate. Select...

BulletProof, yes you are right, there is a possibility to create one NURBS surface for tube. I'm taking another approach. This is the same trick that I use for poly tube.

1. create a torus (8...

This is done with Edit Polygons->extrude edge, with curve to control how the cylinder open. Division is set to 5 to get decent curvature

But unfortunately in the extrude edge with curve, you need...

By default, when you use Surface>Revolve or Surface>Loft, output will be a NURBS surface.
But in your case, probably you have change the default setup on Output section, instead of a NURBS you could...

Modify>Convert NURBS to Polygon

You could uped your resolution if it is necessary, I think maya don't think in dpi, it just in resolution.

3000 x 2400 pixel, will be print as 10" x 8" at 300 dpi.

Best regards,

I'm just shooting in the dark here.

1. You create a material, and assign texture map to it a file texture that has alpha information in it.
2. You can not move the slider in AE for the material....

Differnce in RAM could change the performance dramatically when you render. When the phisical RAM is not big enough to handle the requirement, it start swapping the data out to harddisk which are...