Find the moment of inertia of this system about an axis that is perpendicular to the plane of the square and passes through one of the masses.

We would need to know the geometry of the system. The formula for the moment of inertia about the axis the axis perpendicular to the plane for common geometries are

Solid cylinder: I = (1/2) MR^2

Hollow cylinder: I = MR^2

Solid Sphere: I = (1/12) ML^2

Square Plate: I = (2/3) MR^2 (where R is half the length of the diagonal)