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Like a gesture, a shake can be used as a form of input to your application. For example, the drawing program GLPaint, which is one of the iOS sample code projects, lets users erase drawings by shaking their iOS device, sort of like an Etch A Sketch.
Detecting shakes is relatively trivial. All it requires is checking for an absolute value on one of the axes that is greater than a set threshold. During normal usage, it’s not uncommon for one of the three axes to register values up to around 1.3 g, but getting values much higher than that generally requires intentional force. The accelerometer seems to be unable to register values higher than around 2.3 g (at least in our experience), so you don’t want to set your threshold any higher than that.