"Historically, the investigations of oscillatory motions was motivated by the desire to improve methods of telling time. ...In the seventeenth century the need to measure small periods of time accurately for the purpose of telling longitude at sea caused scientists to search for increasingly accurate clocks. The search resulted in some major successes that were at least as valuable for the advancement of mathematics and the study of other phenomena of nature, such as light and sound, as they were for the specific problem of measuring time. Scientists naturally concentrated on any physical phenomena that seemed to be periodic or repetitive and might therefore be related to the periodic motion of the planets. Two phenomena recommended themselves for closer investigation, the motion of an object or bob... on a spring, and the motion of a pendulum. The first of those attracted the attention of Robert Hooke... Suppose d is the increase or decrease in the length of the spring resulting from extension or contraction. Hooke found that the restoring force the spring exerts is proportional to d; that is, the force is a constant k, say, times d. This is the meaning of [Ut tensio, sic vis ("as the extension, so the force")]..."