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According to Hooke's law,

, the restoring force

of an extension spring is proportional to its linear extension

The value

is the spring constant and depends on the design parameters as follows:

[1]. Here

is the diameter of the coil,

is the diameter of the wire,

is the number of active windings, and

is the shear modulus of the material.

Reference

[1] K. Gopinath and M. M. Mayuram. "Helical Extension Springs." Course notes for Machine Design II at the National Programme on Technology Enhanced Learning, India. (May 14, 2012) nptel.iitm.ac.in/courses/IIT-MADRAS/Machine_Design_II/pdf/4_ 4.pdf.

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Design of a Helical Extension Spring