Understanding Different Accelerations in Constrained Pulley Motion

[anigeo]

could you please tell me how can the accelaration of masses m1 and m2 can be different.
i am in a great necessity.so please explain me how can the two strings of the two sides of the lower pulley have different accelarations?

 

[robphy]

A good start: draw some free-body diagrams.

 

[Pi-Bond]

The lower masses have different accelerations due to the fact that the pulley they are attached to is itself moves due to the mass m₃. So the mass moving upward will have an augmented acceleration while the mass moving downward will have a diminished acceleration. (Everything being viewed from an inertial frame like the constant surroundings.)