I'm hoping someone may a suggestion for the following need. It's to form randomly changing waves in a kinetic sculpture.

I'd like to have essentially a linear motion table that can be positioned at arbitrary positions quickly. The entire range of motion, from one extreme to the other, would only need to be 12 in. At its fastest, 200 cycles per minute would be sufficient but the rate must be controllable. Positioning accuracy is not so important, +/-1/8” accuracy is probably fine. Motion should be fairly smooth. The weight being moved is only a few pounds so the little power is needed.

I’ve considered the standard “screw connecting a motor to a platform” and “motor connected to disk connected to linkage connect to platform.” Unfortunately, the former is slow (though with a stepper motor meets the other requirements) and the latter is requires halting the machine to adjust the position of the linkage (to adjust the range of motion). Would a "server/stepper connected to a platform via a belt" be a possible solution?

Thank you.