How often should a sump pump cycle?
Sump pumps normally have some type of water level monitoring sensor. Very typical is that this is some type of float mechanism that activates one or two switches. The idea behind this sensor system is to turn on the sump pump when the water rises to a certain level. Then the pump should run until the water level falls to some lower level. The better units will have two switches in the sensing mechanism, one which monitors the upper turn on level and another that monitors the lower level. Other cheaper units only have one switch to turn on the pump at the upper level and then use some other scheme to decide when to shut off the pump. That other scheme could be a flapper device, a timed cycle or just hysteresis built into the single sensor switch itself.  

If your sump pump is turning on and off in rapid short bursts is probably means one of three things:


The upper and lower level sensor points are adjusted too close together. As soon as the pump goes on it expels enough water to reach the lower level in a rather short period of time. 
Another possibility is that the sump pit is too small for the water inflow rate and the pump is able to expel all the water in short order even if the sensor points are adjusted properly.
Then there is the possibility that the sump pump is seriously oversized for the size of the pit and can empty in a short period of time. 


From your question details it sounds like the most likely scenario in your situation is the item 1) above.