# Oscillating Systems

Besides planetary motion, another gravitation induced dynamics, extremely relevant for its importance for the foundation and history of concept, measure and mathematical model of time, is the **motion of a pendulum**. As an aside, it is worth mentioning that textbooks are sometimes reporting confusing tautologies about the “operational” definition of time interval and of time measurement units. From one side it is stressed the necessity to find (not define) a “periodic” phenomenon, then the small oscillations of pendulum are found experimentally isochronous using a chronometer. In this way, the important observation of the universal proportionality between periods of different systems oscillating around an equilibrium position is substituted by a tautological definition. We will show that the pendulum motion can be thoroughly examined via the discretisation procedure described for the Gravitational Systems. In particular, the process can be implemented in a spreadsheet and allows to analyse the oscillatory motion of a pendulum, for generic initial conditions, in presence of viscous friction and forcing terms (e.g. the one meant to model the escapement of the pendulum clock).