Kitchen Large Electric Appliances - Radiant cooktop has intermittent dual-burner

I have a ten year old Kenmore glass top radiant type slide-in range with a rear dual burner. The burner is 10-12" diameter on one setting of a front mounted rocker switch but can be changed to a 6-8" burner. No matter the setting of this burner switch, when the burner control is turned on, the burner will heat and glow for approx. 10-20 seconds with a notable hum at the peak of the cycle and then go out. About ten seconds passes and the burner will cycle again in the same manner. Believe me when I say, the large burner heats takes forever to heat a large stock pot of water this way! I have the service manuals on all my other appliances, but never got one for this.