There are two same-but-different technologies that can cause a vibration: A rotational motor, or a transducer. They both operate on the same principle: electricity in a coil makes a magnetic field and that field causes a force on a magnet that causes motion: The motor rotates and the transducer moves in a straight line.
A motor will convert electrical energy into a spinning motion. If you attach an off-center weight to the motor, as it spins it will vibrate. In the motor electricity passes through a coil of wire that creates a magnetic field, and that field acts on a permanent magnet to create torque. The torque makes the shaft spin and you get a vibration. The motor takes time to build up speed and thus can only ever ‘vibrate’ with multiple oscillations by the time power is applied and removed.
The second is a transducer (generic term for anything that converts energy from one form to another), but instead of causing a spin like the motor, it operates more like a speaker with a coil and a magnet on a spring. The coil can nudge the magnet one direction or the other…but instead of being attached to a diaphragm to move air to make sound like a speaker, it just vibrates the mass of the magnet around. The advantage of this method is it can create more nuanced sensations like taps or various frequency sounds. Apple calls their implementation a “taptic engine”, where the vibrations can simulate a clicking switch. Because the mass on the transducer acts nearly instantaneously, and doesn’t need to keep spinning (because it hits the end of travel causing a tap/click) it can create single pulses of motion.
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