This is what I did for my logo animation. We're animating falling objects, in this case, they're hanging by a cord. To create the random movement we use the graph editor modifiers.
For this simple animation, there is no physics needed. I like to put in some extra work using procedural animation with graph editor modifiers. So we can easily reuse the animation. I reused the animation for the different characters in my logo animation.
If you want to know more about the Graph Editor Modifiers in Blender let me know. There is a tutorial for this in the planning.
I'm curious to see what you guys do with this. Tag me at Instagram @mv.artz or include #mvartz in your post.
If you have any question let me know.