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Interpolation to Magnitude Conversion

Hello - I found this forum after spending hours of getting nowhere with trying to solve this on my own =)

I have equations that generate interpolation/tween curves (solid lines in attached picture) - these are used in a computer game to smooth the movement between two points by interpolating a position at any given time between the two points.

Attachment 23888

The red line describes linear tweening, so the object moves with a constant speed between the two points.

The blue line is a cubic ease in/out equation, so the object starts moving slowly, then accelerates, then slows down before reaching the destination.

What I am trying to figure out is if I can use these easing equations (or the resulting values) and convert it into a magnitude instead (illustrated as dotted lines in picture.) I would like to use the same easing equations to multiply with an oscillating wave to make the magnitude of the wave follow the same type of ease in/out characteristics.

First of all, does my question make sense... and more importantly, is it possible to make such a conversion?

Thanks in advance.