Need help choosing mechanical device to use for rocking a cradle

I was hoping to build something similar to this for a cradle (minus the mechanical clock system):

And was wondering if anyone had any ideas on how I'd be able to quietly move it back and forth. I should mention that I'm a coder but I don't have much experience with electronics, so the less parts, the better, but I'm willing to learn. I'd probably use an RPi to trigger the Arduino to turn it on/off, but it would be ideal if it could all be done through only the RPi. Thanks in advance for any input.

I'm also open to other cradle designs as well if there is something that may potentially work better.

The whole point of that video is to illustrate the clock-like mechanism.

Can't you just draw a simple diagram of the machine you want to build? And how much force will be needed to make it move?

Maybe you can move it with a very low-geared DC motor and a crank.

...R

I am thinking automotive widshield wiper motor. Control it with a logic level MOSFET, Solid State Relay or (less favorable) mechanical relay.

simple crank is all thats needed, gear down a motor to drive a shaft at the rocking rate, crank (can be elastic
band even - very smooth start) transmits rotation to side-to-side motion. Expect to need to adjust the speed to match the rocking frequency depending on distribution of mass.