Someone gave me of those "shake lights" a while back as a gift -- Christsmas or my birthday. It was made very cheaply -- a novelty really -- and it didn't last long as it couldn't stand the shaking necessary to power it. As near as I could eyeball, a tiny little lead of magnet wire from the coil broke, and thus ended that particular linear alternator design.

It was simple a permanent magnet that slid back and forth inside a coil. The changing flux induced an EMF which charged a capacitor which powered the LED array light.

It would be a handy thing if designed ruggedly, but this was just a gimicky thing -- like those "Ronco" gadgets that saturate the airwaves at Christmas time.

-Richard