spiral tilt window balance?

A home owner from South Portland, ME says:
Vinyl casing, 22 inch length is 1/2 inch diameter and coil inside is ?". Not sure if side makes a difference, but left side spiral seems to be broken within the vinyl casing. Window would not move up and was detached from pivot shoe. We purchased the house in 1998 and renovated in 2002, but I am pretty sure we did not replace this particular set of windows, so I am not sure the exact date of installation other than most likely in the '90s. If you do not have the same part, is it possible to install a replacement spiral tilt balance and pivot shoe?
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Casey from SWISCO responded:

Hello,

Your spiral balance resembles either the 3/8" diameter S900-22 or the 5/8" diameter S600-22. I would recommend double-checking your diameter since these balances were not made in 1/2" sizes to our knowledge. Keep in mind that the diameter is determined by the size of the plastic housing on your original balances. 

If you'd like to replace the pivot shoes as well, we would need to see yours uninstalled, as well as confirm the exact width and thickness to compare to our inventory. Thank you! 

A home owner from South Portland, ME says:
Thank you for the reply. I did send pic of pivot shoe in original text. My broken window balance is cased in ½ inch diameter vinyl (not aluminum or metal as your appears to be) around the coil that is ? inch diameter. I am guessing that if I purchase a window balance, it already has a matching pivot shoe or are pivot shoes universal to the balance but sold with different dimensions to accommodate the internal window casing? My pivot shoe currently is 2.25" tall, ½ inch deep and roughly 1 inch wide (not easy to measure while in track). Also pivot shoe has 550C on it..not sure if that helps identify it. My guess is the 3/8" diameter S900-22 would work, but I am second-guessing the corresponding shoe that appears to go with it. It would seem that the width is the most important measurement to fit it to my window casing. Thank you for your assistance.
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Casey from SWISCO responded:

As we mentioned, we would need to see your pivot shoe fully removed from the window to compare it to our inventory. You are correct that the width and thickness are the most important dimensions to ensure that whatever we recommend would fit in your window channel, which is tough to measure with the shoe still installed. Also, spiral balances are not compatible with one particular pivot shoe. See the video below to help with the removal process. 

As for the balance, only style spiral balances often used the plastic covers shown in your photos but manufacturers moved over to using all metal housings since the covers tend to become brittle over time. Also, these balances were not made with 1/2" diameter plastic tubes to our knowledge but the can become tough to measure over time since the plastic can become misshapen. You may want to check another balance to confirm if the plastic tube matches our 3/8" or 5/8" replacements. 

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