Water well pump surging on and off, from its low limit to its high limit,when the water is turned on, why...?

This well has run fine for years. Now its surging on and off quickly,when you run water from it. How do I test limit switch?,bladder bag? or am I on the right track. Pressure when no water is on is about 40lb, when you turn it on it goes from aprox. 30lb to aprox. 52lb in just a second, these being the lower and high limits it (the pump) turns on and off steadily. Thank You for any help you can give!