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Like, in a GIF with 20 frames, morphing from a dog to a cat,
both the First and Last frames might show for one entire second.  
I'd like Frames 2 thru 19 (each for 0.1 seconds) to "shake", like in an earthquake.
Can GIMP make that happen?
Thanks, people.

Gimp can do a lot of things if you are willing to do some hand editing   Earthquake effect & automatic ? There might be a plugin somewhere.  For example you might be able to replace the morph with a transition effect dog to cat.

I can throw this in as a starter, Cat to Dog morphed (somewhat) over 20 frames. Then the intermediate frames with a effect applied using a Gimp plugin gmic from http://www.gmic.eu The advantage of this is the same effect can be applied over a number of frames. Looks like this.

[attachment=7428]

To get some variation, applied to odd numbered frames (visibilty on) the settings changed then applied to even numbered frames. 

quick example: 

[attachment=7429]

At that point you would be better off with a video editor and a decent special effects palette, and then convert the video to GIF at the end.