Motion on the Springs of a carriage body

Extract

In continuation of the Mathematical Gazette, p. 389, September 1914, on Linear Dynamics, the investigation is resumed here of the rolling and pitching of the body of a carriage on the springs, such as experienced in a railway carriage, tram, or motor car, and the effect can be studied as realised ; but most instructively in the motibus, where the action is felt on a more violent scale, vibrating with dynamical interest and poetry.

1. Begin by supposing the carriage body lowered down and deposited on four springs at the corners of a rectangle, sinking down vertically on the springs an equal distance c suppose, the permanent average set of the springs.

A vertical oscillation of the body will then synchronize, as on p. 393, with a simple equivalent pendulum of length c, assuming the Law of the Spring (Hooke's, the Linear Law).