Imagine a thin rod. Anchor one end rigidly, and attach a lever that rotates the bar about its own axis to the other end.
You can use the lever to twist the rod, a bit. If you let go, it springs back. This is a type of spring called a torsion bar.
If you make the rod longer you can twist it more. More elastic. And so on if you make it longer and longer. But very long very elastic torsion bars get cumbersome.
So wind the torsion bar into a cylinder – the cork screw shape as you call it – you now have a coil spring. A very long torsion spring in a small space, gives you that elasticity you see.
It’s not about the shape of the spring, but about the length of the spring.
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