I have a submersible well pump. It is short cycling. My water pressure quickly drops and then increases very quickly for a few seconds while the pump is running, This occurs every few seconds with the pump pressure switch turning off and on. What is the problem?

The tank is under pressurized or bad. Tap on the bottom of the tank to the top it should sound hollow about half way up. If not the bladder is more then likely shot. A check valve or foot valve could be a problem also losing prime on the pump and the pressure switch keeps cycling. Another way to tell if the bladder is going bad is when the well kicks on the well pressure gage jumps around while pressurizing

Here's a check list to test and pressure the tank.

Bladder Type Water Storage & Pressure Tanks - Diagnosis & Repair

Water tank air bladder pressure settings: How to Set or Adjust the Air Pressure in Bladder Type Water Storage & Pressure Tanks

This site should narrow it down if not help correct the problem Get back to let us know how it goes.

Nick, it is either a checkvalve or (more likely) a bad bladder tank. The way to tell the difference is simple. If the pump cycles when no water is being used(in other words, all the time), then suspect the check valve. If it only cycles when water is being used in the house, then the tank is bad. Press the little air valve at the top for a couple of seconds. If water comes out, then you have found the culprit. Replacing the tank is the only real cure. If you need to "buy" a little time, you can drain the tank and then put air in it through the valve on top. That is not a long term fix, but it will get you by for a few days until you can take care of the problem.