My apologies for the delayed response.
I still can't see how the tension of the string is able to exert a horizontal force on M1 if there is no friction between them (specifically, the horizontal bit over the pulley). I'm not sure how the vertical bit of string would exert a force either...
Homework Statement
For context, the first question for this diagram asks for the force F on m1 needed to keep m3 at a constant height.
The second question (which I'm struggling with) asks for the acceleration of m1 in the case where the force F=0.
All surfaces are frictionless and I've...