Water pump burps every 35 to 40 seconds for 2 to 3 seconds

It sounds to me like you have a pressure switch problem. Is the pressure switch built into the pump? The low pressure on is set to close to the high pressure off. The pump is cycling. Pluging the outlet at the pump only makes this worse. Most plumbing systems have enough piping length to act as a accumulator. Is the new pump any larger in voluum than the old pump?