frigidaire glasstop stove element turns off and on during use
Smooth-top (ceramic) stoves can be damaged if an element gets too hot. To prevent this, each element has a thermostat which cuts off the heat at a certain temperature. It probably won't happen if you have a properly-sized pot of water heating up, but if you put the element on high with no pot then the element will definitely start cycling off and on at some point.