Second's Pendulum

A second's pendulum is defined as a simple pendulum whose period is exactly two seconds, $T=2$ s (so that it completes half an oscillation, and hence ticks once, every second -- historically the basis for many mechanical pendulum clocks). Substituting $T=2$ s into the period formula $T=2\pi\sqrt{L/g}$ (Eq. 5.28) and solving for L,

where $L_s$ denotes the length of a second's pendulum. This relation is genuinely useful in both directions: if the local acceleration due to gravity g at some place is already known, Eq. (5.30) predicts the length of pendulum that will tick seconds there; conversely, if a pendulum is experimentally TUNED (by adjusting its length) until it does correctly tick seconds, its measured length $L_s$ can be used to determine g at that location -- a classical, very precise method of measuring g. …