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.

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 presented as an audio input value, baked to FCurve, 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.

NOTE

-(Since it is a concept demonstration, it is kept as simple as possible.) The GeoNodes trees are kept clean, the nodes are not contracted into node groups for easier readability and have detailed explanations. You can embellish, refine as you wish.

-(The files are working in Blender 3.6X AND ABOVE utilising the Simulation Zone feature)