In a well-made movement (the technical term for the clockwork of a music box or a watch, the stuff that keeps time), there will be a flywheel which resists increasing the motion of the gears beyond a maximum speed. Past that speed, the pressure from the wound-up spring just adds more potential energy to the flywheel. Effectively, the flywheel and spring together act as a mechanical battery, storing energy for use. The stored energy is released as the gears turn. Once the flywheel slows down enough, it is no longer capable of maintaining the minimum speed, so the music box slows down and stops. The slowdown is actually less abrupt than you give credit for in most cases, it just feels abrupt; it usually takes 5-10 seconds to completely wind down and stop once it’s below speed cap.
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