How to make a Pendulum transition in After Effects?

Question

Adobe After Effects

Hello, for the first time on the forum, I can’t find the answer to my question for a long time, but I can’t implement what I specifically want myself. Looking for help here, hope for any clue.

You need to make the transition "Pendulum" (Or Pendulum, as you like), as from the "Cap Cut" video editor. Here is a video example of what exactly I would like to bring to life (0:42 - 1:10) youtu.be/YNDj_S0Flo4

My problem is that I can not achieve the same smoothness, no matter how many graphs I try, no matter what effects from Sapphire would not use. Always the result did not suit me, but I like the transition, I would like to learn how to do it.

If someone somehow had the same problem as me, and this person will have an answer to my question (you can even just leave a guide from YouTube or from other sources), I will be very grateful for any shred of information.