Huygens’ cycloidal pendulum: an elementary derivation

Abstract

A pedagogical derivation of the Huygens cycloidal pendulum, suitable for undergraduates, is here presented. Our derivation rests only on simple algebraic and geometrical tricks, without the need of Calculus.

Kissing the cheeks of Huygens

“…Table 1 shows large-displacement data for three measurements of a pendulum swing against the set of small cheeks: one with a matching pendulum length of 25 cm, a second one with a too short length of 12.5 cm and third one with a too long length of 56 cm. The data illustrate that the cheeks undercompensate in case of a too long pendulum and make the period larger than the theoretical small-angle period computed with formula (5). In case of a too short pendulum, the cheeks overcompensate and the period becomes less than the theoretical small-angle period.…”

“…Then the period gets smaller (because the period increases for larger initial amplitudes, this increase is compensated).' A calculus-based derivation of the isochronous property of cycloidal pendulum of Huygens requires too advanced mathematical concepts and techniques for secondary school students, but not for undergraduate physics students [5]. We discuss this in the next section.…”