Atwood's machine principle

Actually, for free falling of body, to determine the acceleration of body we can apply laws of motion, but the time is too short for free falling body.
In Atwood's Machine, mass m2 is considerably retarded by the mass m2, therefore the unbalanced resultant force on the system to be considered as
F=(m2-m1)g------1
The net accelerated mass is M=m1+m2-------2
Therefore the acceleration of the system is
This is the Atwood's principle to determine the acceleration due to gravity