# Seconds pendulum

Longcase clock with a seconds pendulum.
The seconds pendulum, with a period of two seconds so each swing takes one second

A seconds pendulum is a pendulum whose period is precisely two seconds; one second for a swing in one direction and one second for the return swing, a frequency of 1/2 Hz. A pendulum is a weight suspended from a pivot so that it can swing freely.[1] When a pendulum is displaced sideways from its resting equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position. When released, the restoring force combined with the pendulum's mass causes it to oscillate about the equilibrium position, swinging back and forth. The time for one complete cycle, a left swing and a right swing, is called the period. The period depends on the length of the pendulum, and also to a slight degree on its weight distribution (the moment of inertia about its own center of mass) and the amplitude (width) of the pendulum's swing.

At standard gravity its length is 0.994 m (39.1 in). This length was determined (in toises) by Marin Mersenne in 1644. In 1660, the Royal Society proposed that it be the standard unit of length. In 1675 Tito Livio Burattini proposed that it be named the meter. In 1790, one year before the metre was ultimately based on a quadrant of the Earth, Talleyrand proposed that the metre be the length of the seconds pendulum at a latitude of 45°.[1] This option, with one-third of this length defining the foot, was also considered by Thomas Jefferson and others for redefining the yard in the United States shortly after gaining independence from the British Crown.[2]

In 1670 the seconds pendulum was employed by William Clement in his improved version of the original pendulum clock by Christiaan Huygens, creating the longcase clock which could tick seconds.[3]

## Length of the pendulum

${\displaystyle T=2\pi {\sqrt {\frac {l}{g}}}}$.

The length of the pendulum is a function of the time lapse of half a cycle ${\displaystyle T_{1/2}}$

${\displaystyle l=g\left({\frac {T_{1/2}}{\pi }}\right)^{2}}$.

Being ${\displaystyle T_{1/2}=1\ \mathrm {s} }$ and ${\displaystyle g=9.81\ \mathrm {\frac {m}{s^{2}}} }$ therefore ${\displaystyle l=0.994\ \mathrm {m} }$.