constant force coil spring and a plastic pivot shoe (or sash carrier) used in a double-hung tilt window balance system.

We should be able to assist you, but I can't determine what you have based on these photos alone. We actually do need to see the pivot shoe, but it's not pictured here. The pivot shoe is the square or rectangular plastic block that the springs clip onto at the end. It's likely still in your window, but we will need to see it removed.

Pivot shoes act as a kind of "key;" once I see that, I can tell you everything else that's needed for this assembly.

These appear to be the same photos as before. As I mentioned previously, the pivot shoe is not pictured here. It is the square plastic block that goes under this assembly in the window.

Thank you! This pivot shoe looks similar to our 15-228. I think this might be what you want, but look it over to verify.

This is compatible with two different sized springs: the 3/8" Series 165 and 1/2" Series 160. Based on your previous photos I would wager that you have the 1/2" version, but you should measure to be sure.

Assuming I'm right, I'd recommend the Series 160 coil spring and 15-150S support.