Seconds pendulum

When released, the restoring force combined with the pendulum's mass causes it to oscillate about the equilibrium position, swinging back and forth.

For a simple gravity pendulum — a point mass on a weightless string of length

where g is the acceleration due to gravity, with quantity dimension of length per time squared.

Using the standard acceleration of gravity g0 = 9.80665 m/s2, the length of the string will be approximately 993.6 millimetres, i.e. less than a centimetre short of one metre everywhere on Earth.

[2]: 2.6 The pendulum clock was invented in 1656 by Dutch scientist and inventor Christiaan Huygens.

[3][4] Galileo had the idea for a pendulum clock in 1637, which was partly constructed by his son in 1649, but neither lived to finish it.

[5] The introduction of the pendulum, the first harmonic oscillator used in timekeeping, increased the accuracy of clocks enormously, from about 15 minutes per day to 15 seconds per day[6] leading to their rapid spread as existing 'verge and foliot' clocks were retrofitted with pendulums.

These early clocks, due to their verge escapements, had wide pendulum swings of 80–100°.

In his 1673 analysis of pendulums, Horologium Oscillatorium, Huygens showed that wide swings made the pendulum inaccurate, causing its period, and thus the rate of the clock, to vary with unavoidable variations in the driving force provided by the movement.

The increased accuracy resulting from these developments caused the minute hand, previously rare, to be added to clock faces beginning around 1690.

[8]: 193–195  With these improvements, by the mid-18th century precision pendulum clocks achieved accuracies of a few seconds per week.

[9][16] However, it was soon discovered that the length of a seconds pendulum varies from place to place: French astronomer Jean Richer had measured the 0.3% difference in length between Cayenne (in what is now French Guiana) and Paris.

[18] Instead of the seconds pendulum method, the commission of the French Academy of Sciences decided that the metre measure should be equal to one ten-millionth of the distance from the North Pole to the Equator (the quadrant of the Earth's circumference), measured along the meridian passing through Paris; in 1983 the unit was defined as the distance light travels in 1/299,792,458th of a second.

[19]: 111 The idea of the seconds pendulum as a length standard did not die completely, and such a definition was used to define the yard in the United Kingdom.

More precisely, it was decided in 1824 that if the genuine standard of the yard was lost, it could be restored by reference to the length of a pendulum vibrating seconds at London.

[21][22] Defining a length by Talleyrand's method, 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.

The second pendulum, with a period of two seconds so each swing takes one second
A simple pendulum exhibits approximately simple harmonic motion under the conditions of no damping and small amplitude.
The second pendulum clock built around 1673 by Christiaan Huygens , inventor of the pendulum clock. Drawing is from his treatise Horologium Oscillatorium , published 1673, Paris, and it records improvements to the mechanism that Huygens had illustrated in the 1658 publication of his invention, titled Horologium . It is a weight-driven clock (the weight chain is removed) with a verge escapement (K,L), with the 1 second pendulum (X) suspended on a cord (V). The large metal plate (T) in front of the pendulum cord is the first illustration of Huygens' 'cycloidal cheeks', an attempt to improve accuracy by forcing the pendulum to follow a cycloidal path, making its swing isochronous. Huygens claimed it achieved an accuracy of 10 seconds per day.
The delay curve—above the axis a sundial will appear fast relative to a clock showing local mean time, and below the axis a sundial will appear slow .
Drawing of pendulum experiment to determine the length of the seconds pendulum at Paris, conducted in 1792 by Jean-Charles de Borda and Jean-Dominique Cassini . From their original paper. They used a pendulum that consisted of a 1 + 1 ⁄ 2 -inch (3.8 cm) platinum ball suspended by a 12-foot (3.97 m) iron wire ( F , Q ). It was suspended in front of the pendulum ( B ) of a precision clock ( A ).