I have had my faucet in the kitchen for a couple of years and today for no apparent reason the water (hot and cold) pulsates when turned on. How can I repair it?

Sounds like your diverter's vibrating. This can be caused by low pressure or a piece of trash caught down in there. The diverter's located under the spout ,(see images) Shut the water of under the sink and remove the spout. Check and clean the diverter and then place a pan over the open valve and turn the water back on to flush everything out. Good luck, Tom