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There are many mechanical systems that exhibit ranges of negative differential resistance. In fact, this is a common design element in systems that are designed to have "detents" or a "positive action" or a "click." A good example is an ordinary toggle switch (or a key on a computer keyboard), which, as the handle is moved from "off" to "on", initially presents a firm and increasing downward force. As the center point is passed, a zone is entered in which the downward force decreases, which feels like a "sudden" yielding. This is often referred to as a collapse action mechanism.
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