balances

I'm working on some windows that have some sort of long spring that attaches to the window sash and to a narrow pivot shoe. The top of the breaks over time (it's plastic) it's a pretty common problem with these windows but I cannot identify the parts if they are available or if they can even be replaced. I had to pry it out pretty hard just to remove the broken shoe and spring. I attached some photos of the broken parts as well as one with the spring & pivot shoe still intact. Please let me know if you guys know what make/type of windows these are. (They are double hung, tilting windows). I can measure the spring lengths as they vary depending on the size of the windows but the pivot shoes are all the same. Thanks!