Wiggler Dynamics
The Wiggler Dynamics Geometry Node is a simple setup that will add some dynamic 'jiggle' to your Blender animations. It uses the Simulation Zone in a Geometry Node tree to make a Target object follow a Control object in a dynamic way. The file has a complete setup using Empty objects, but you could recreate the relationships with objects of your own. The simplest way to work with it is to use the supplied configuration.
There are two copies of the Blender file. One for Blender 3.6, and another for Blender 4 and up. The setup is the same in each, some of the nodes just needed to be reconnected when it was opened in v3.6.
Usage
Append the "Wiggler" collection from the supplied .blend file.
This will add the collection, and three objects to your scene: Wiggler_Control, Wiggler_GeoNodes, and Wiggler_Target.
If you want multiple copies of the setup in your file, you can right-click on the collection, and 'Duplicate Collection'. This will copy the entire setup, with all the pieces connected properly.
The 'Control' Empty object will move the setup around. The 'Target' Empty is driven by the 'GeoNodes' object, and will dynamically track the Control.
The Geometry Nodes Modifier on the 'GeoNodes' Mesh object has settings that control the behaviour of the system. There is also a switch to Enable or Disable the Dynamics.
Experiment with different values to see the effects that they have. The simulation can be made to follow the control object closely or more loosely, depending on the Stiffness, Acceleration, and Damping values.
When the Control object is moved, the Target object will follow along.
You can incorporate it into a rig quite easily. Parent or constrain the Control Empty to one of the bones. Then you can constrain a different bone to target the 'Target' Empty object. In the second video on this page, the control is parented to the lower blue bone, and the upper green bone uses a Damped Track constraint to point towards the target object.
You will get a zip file with copies of the Wiggler Geometry Node setup for Blender 3.6, and Blender 4 and above.