Compositional heterogeneities of cell membranes are thought to play an important role in many physiological processes. We study how variations in the membrane composition can be driven by nonthermal fluctuating forces and therefore show how these can occur relatively far from any critical point for the membrane. We show that the membrane steady state is not only controlled by the strength of the forces and how they couple to the membrane, but also by their dynamics: In a simple class of models this is captured by a single force correlation time. We conclude that the coupling of membrane composition to normal mechanical forces, such as might be exerted by polymerizing cytoskeleton filaments, could play an important role in controlling the steady state of a cell membrane that exhibits transient lateral modulations of its composition on length scales in the 10-100 nm regime.