Hey f,
Frequent cycling is a sign of a low Freon charge. Often when the system is left unused during the winters Freon will seep out of the compressor seal. When it is brought into use again during warmer weather the charge is adequate enough to provide cool air when the ambient temperatures are not too high. (70s and low 80s).
The low charge does however signal the low pressure cycling switch to open and disengage the compressor. With the compressor disengaged the pressure in the system equalizes between the high and low side. The pressure then is adequate enough to close the LPCS, and the compressor engages. This continues as the compressor sucks Freon into the low side. It passes the expansion valve. It boils, becomes a low pressure gas and when not sufficient enough to maintain the required low side pressure the LPCS opens, disengaging the compressor...the cycle continues.
Here in Florida many places will check for leaks for free or a minimum charge. Some states have a policy that makes it illegal to add Freon to a system known to have a leak. (don't know where you are.)
There are some good DIY Freon recharge kits now available at most part store and Big Box stores. Just remember in AC...enough is good...more isn't better...Don't overcharge!
Good Luck