This is an example setup for a hexagonal distance-based displacement with an inertial after-wave effect (aka "Wiggle Deformer") in Geometry Nodes.

Video demo here and here.

The aim of the setup is to provide a quick, easy to read and reuse example for an effect, such this.

The steps are clearly labeled and explained. They include the creation of the hexagonal grid, it's separation into rim and inside faces, the displacement nodes (which here are driven by an audio value, baked to F-Curve, but they can be manual or any animated value), and the "Wiggle Deformer" node setup, which simply registers the difference between the previous, displaced positions and the current one, then adds them to the mesh as a new velocity vector, scaled by a user input value frame-by-frame.

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NOTE

-(Since it is a concept demonstration, it is kept as simple as possible.) The GeoNodes trees are kept clean for easier readability and have detailed explanations. Everything is built from the base. The point of these setups is to provide a base core of the concept, node from node, instead of contracting all into node groups with exposed settings, which makes everything harder to read and dissect.

You can embellish, refine as you wish based on the core or realize your own ideas.

-Read the text description, it has a lot of useful info !