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I'm not sure how practical this will be.

The magnet in a shake-light is large, and the coil probably has at least a hundred turns of wire. A magnet and coil that can fit into a battery is going to be much smaller-- and then you still have to fit in the rectifier and capacitor.

All of this in the AAA form factor? Implausible.

Not really. You can see a smaller homemade version of the shake light here: http://www.instructables.com/id/Shake-it-like-a-Tic-Tac!/

That could almost fit in a AAA. The capacitor or battery would be the largest part after the magnet/coil mechanism.

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