Sounds like you have a glass top electric coil stove, not induction. Induction has a very stable fast heat, cooks like gas. Glass top electric are the one that turn on for 10 seconds off for 30, never the right temp.
I replaced a glass top stove with an induction one last year, couldn't be happier. I can actually fry eggs now.
It is a tabletop induction burner, not a glass top electric coil. Its cycle frequency is about 60Hz, I can time it by the coil whine.
Low quality ones generally have that problem due to using PWM to control the temperature. I've used cheaper and more expensive ones, and the more expensive ones have much more fine control of temperature, and not just a toggle between on and off.
Absolutely unmatched for boiling water, and I'm very happy using it with a cast iron dutch oven for slow cooking and soups or stews.