where F is the resisting force, D is the displacement, and the k is the spring constant.

For a non-linear spring, the resisting force is not linearly proportional to its displacement. Non-linear springs are not covered in depth here.

Circular cross section springs are shown. If space is limited, such as with automotive valve springs, square cross section springs can be considered. If space is extremely limited and the load is high, Belleville washer springs can be considered. These springs are illustrated below,

Leaf springs, which are illustrated below in a typical wheeled-vehicle application, can be designed to have progressive spring rates. This "non-linear spring constant" is useful for vehicles which must operate with widely varying loads, such as trucks.

The eighteenth century dawn of the industrial revolution raised the need for large, accurate, and inexpensive springs. Whereas clockmakers' springs were often hand-made, now springs needed to be mass-produced from music wire and the like. Manufacturing methodologies were developed so that today springs are ubiquitous. Computer-controlled wire and sheet metal bending machines now allow custom springs to be tooled within weeks, although the throughput is not as high as that for dedicated machinery.