Vinyl Window No Markings

A handy person from Aberdeen, NJ says:
The windows are approximately 59" x 36" double paned builder-grade vinyl windows. There are two windows not staying up. One of the windows does not appear to have the piece shown with the tape measure above at all. Are the window steel tabs suppose to go into the locking /turning mechanism of the plastic part of the coil or the square slot above the locking/turning mechanism.

Most of the videos I have seen show a slot leading to those coil so they can be dropped in from above. Mine have no such slots so the steel tabs of the window seem to need to be inserted laterally which seems impossible?

If you need anything more to determine my parts let me know. Thanks for your help.
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Tom from SWISCO responded:

The hardware you're showing me is called a coil balance system. Coil balances are precisely calibrated spring mechanisms that go on either side of the window and keep the sash up when you raise it. They produce a constant force that's always counterbalanced by the weight of the sash, hence their name: "balance."

Yours in particular is an older style that isn't made anymore, but we can still help. Assuming you only needed the coil spring itself, you can use our Series 190. You'll note that there are many options for this coil so you'll need the stamp printed off the old one to confirm the best match.

As for installation, you actually do have a slot in your track. I can see it in your fourth and fifth photos. It's not a lot of clearance but it should suffice. 

A handy person from Aberdeen, NJ says:
The spring is stamped 832. However, the plastic part that the coil is attached to is missing on one side. My guess is someone tried to repair the window and took the part out and never replaced it. Are there any plastic housings that would fit my window?
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Tom from SWISCO responded:

Sure, are you talking about the clip/cover you show in your last two photos? That's our 15-186. You'll also want a new 15-182 bushing to help hold the spring to the clip.

A handy person from Aberdeen, NJ says:
You asked that check my old coil for a number. What does the 832 stamp on my old coli spring translate to in your Series 190 coils?
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Tom from SWISCO responded:

Sorry for overlooking that detail. You can use the S190-840 in that case. That should work perfectly well.

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