Does anyone have any insight as to how I could draw a spiral spring (like these unwinding?

I have discovered how to draw an Archimedean spiral ( and a Logarithmic spiral (, but this is a bit more complex. The constant is the length of the spring, and the tighter it is wound, the more loops. I tried using a rotating radius, rotating it more degrees and shortening it as I drew depending on the tightness, but that doesn't quite work. Any ideas would be much appreciated.