Unlike wiggle, shake appears to complete all its work in the first cycle, as seen on the counter section of the timer/counter in the upper left. Once the counter reaches "2", shake no longer has an effect, and can be stopped.
A shake can be either global or local. A global shake affects all unlocked, non-frozen sidechains. A local shake affects only certain sidechains.
In the original interface, starting "Shake" from the actions menu or using the "s" keyboard shortcut performs a global shake. Right-clicking (or control-clicking) on a segment and selecting "Shake" from the wheel menu performs a local shake, shaking only the sidechains within the same secondary structure.
For example, if you click on a segment of a helix and select "Shake", the shake only affects the segments in that helix.
In the selection interface, if segments are selected, shake is local, affecting only the selected segments. If no segments are selected, a global shake occurs.
As with most Foldit tools, it's not clear exactly how shake works. If sidechains are visible (see View Options), they'll usually move around during a shake.
The wiggle sidechains tool can be used to make finer adjustments to sidechain position.