God that diagram took forever to make, and I added too many arrows. Basically, assuming negligible spring weight, the force from the compressed spring is D. So the force wall has to produce the equal and opposite force C.
In a normal world the acceleration of the entire setup would be C - D, and since C = D this would just stand still. But because we have bullshit ninja magic, D just vanishes into the aether. So C is unopposed and just accelerates the whole thing.
At least in space. On the ground, C has to be large enough to overcome gravity and friction.
(A and B were there so I could treat the spring as a separate element, but I realized they're stationary relative to each other and have to be equal, so all I'd be doing is finding the portion of the force that accelerates the spring separately. Which doesn't really matter.)
We might be able to get away with dropping the spring entirely, and using the tension in the crossbar as a spring, but this is easier to imagine since we're making that application of force explicit.
If this is hard to imagine then imagine the thing as made of Jello. you compress the spring against the force-wall, the spring expands and pushes out. The wave travels out through the frame until it pulls the seals forward. The force-wall then moves with the seals exerting whatever force it needs to to recompress the spring.
More rigid frames would just do this so fast it becomes a uniform pressure from the force wall on the entire system.
Also, force walls seem to last a long time so this might answer the Nara question on how to stick point defences up in the air.
They'd drift with wind, and we'd need to compensate for that somehow and have to find a way to keep them floating at the same height. But keeping them pointed up despite small shifts in position is trivial, few off center pads the press against the force wall more as the floating machine tilts in the direction of the offset and you get an automatic counter-rotation.
Edit: The height thing is actually doable too. If you have
low-pressure air cavities pressing against the wall, then the higher you go (as air-pressure outside decreases) the less force they'd exert. Bias it with some of the springs and the thing will float at whatever height has some particular air pressure.
The horizontal movement thing is hard though, the best I've got is some beast of an IMU type setup that is way outside of our tech base.
Edit 2: Wait, we can just use cables that hold them over a particular point in the ground.
It'd mean the setup would also have to hold the cables up, so you need springs under higher tension. Also you'd have to have cables tied down everywhere, messing up the skyline by adding too many sky-lines.
