There are multiple ways. Here are 2 of the more common.
1. An unbalanced motor is spun. To see how this works, take a small object with a hole on one of its ends. Like a nail clipper, or a toothbrush. Now insert a toothpick in the object’s hole, grab the toothpick and rotate it. Your hand will be pulled in different directions by the rotating toothbrush. A cellphone does the same just way faster.
2. The other kind of vibration is with 2 magnets next to each other. Take 2 magnets and a piece of cardboard. Place magnet 1 on top and magnet 2 underneath the cardboard so they can influence each other magnetically. Now grab the bottom magnet and rotate and or move it randomly. You will notice the cardboard vibrate. Inside a cell phone one of the magnets is attached to the phone body and the other is an energized coil, similar to a common speaker.
NOTE: speakers vibrate so fast you can hear them, so a speaker is just a fancy vibrator
Everyone saying it’s a motor spinning an unbalanced weight is a few years behind the curve.
Most modern phones use a linear actuator. The simplest explanation is it’s a magnet that can move back and forth on a spring in a straight line. It then has an electromagnet that can turn off and on at a harmonic frequency causing each oscillation to be a bit bigger than the one before. (Like pushing someone on a swing). Anytime the magnet changes directions it has to push back on the body of the phone which we feel as a vibration.
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