Half Atwood Machine

A block of mass M1 is sitting on a frictionless table. It is connected by a massless string over a massless and frictionless pulley to another block of mass M2.

(a) Build free-body diagrams for each of the masses and write equations of motion for each object. Use the coordinate x1 shown in the figure for the position of mass M1 and coordinate y2 shown in the figure for the position of mass M2.

(b) Use these equations of motion to obtain the acceleration of the two objects. Explicitly state any conditions that you are applying to solve the equations.