Seconds pendulum

As a second pendulum is called a pendulum for a half-wave ( in horology " strike" called ) requires exactly one second. As it did not yet have accurate clocks, it has been used for measuring short time intervals and for physical testing. From the 17th century they took advantage of it for accurate pendulum clocks, and in particular observatories for determining time and for the precise measurement of Sternörtern.

The length of the seconds pendulum is about a meter, which is why the Paris Academy in 1790 discussed whether it would be suitable for meter definition. The period of oscillation is independent of the mass of the bob, but is influenced by the prevailing gravity. Therefore, the second pendulum depending on the latitude of the location from 99.1 to 99.6 cm in length.

Mathematical pendulum

The theoretically ideal pendulum would be a point mass at the end of a massless rod which oscillates at infinitely small amplitude about a frictionless axle. On the 45 ° latitude this mathematical seconds pendulum has a length of 99.4 cm. This length results from the fact that the period of oscillation of an ideal pendulum depends only on its length and the acceleration due to gravity

The length of the pendulum required is a function of the duration of a half-wave

With and so obtained.

The value of g = 9.806 m / s ² applies only to sea-level and middle latitudes to. At the equator it is 9.7803 and 9.8322 at the poles m / s ².

The formula given period of vibration is a linearization of the equation of motion. It only applies to a simplified mathematical pendulum with infinitely small oscillation amplitude, which is not strictly physically possible. Also neither mass distribution ( center of gravity of the pendulum bob ) are still considered amplitude error. For the rough estimate of the length of a Uhrpendels However, the formula is practical.

Influence of the oscillation amplitude

The linearized formula (without the higher order terms ) deceives the user before a isochronism, as if for different oscillation amplitude (amplitude) would apply the same period. The calculation error of this small angle approximation is an operating amplitude of 120 arcmin (2 °) at 0.02 %, but may go far in decaying oscillation in the percentage range. A clock pendulum with a vibration amplitude of 31 ° would lose a day compared to a same clock that vibrates with amplitude of 30 °, 100 seconds. The amplitudes of 11 ° and 10 °, this value is 35 s For small vibration amplitudes, the amplitude error is thus negligible for domestic use.

The seconds pendulum has generally prevailed in precision pendulum clocks as frequency standard. When they could by precise mechanics of Uhrhemmung reduce friction and keep the amplitude constant, the accuracy increased to a few millionths. The second hand was connected to the shaft of the escape wheel, so that it jumps to the next exactly with the pendulum and the eye -ear method of measuring time considerably refined.

By special design tricks such as compensation of thermal effects, evacuation and systematic suppression of external interference accuracies than a tenth of a second per day could be better achieved in the 18th century, which was not surpassed until 1930 by the first quartz watches. Around this time, but also reached the nearly frictionless Shortt clocks already 0.01 s / day.

With the introduction of the meter a definition of this length dimension by one seconds pendulum at 45 ° N was originally planned; a more precise geodetic definition ( 1 m = 1/10.000.000 the length of the meridian passing through Paris quadrant ) was instead the introduction of the meter in 1793 but used because of the earth's shape already an ellipsoid was suspected.

History

Experimental studies to determine the length of the pendulum took Marin Mersenne (1588-1648), Jean -Charles de Borda (1733-1799), Jean -Baptiste Biot (1774-1862) and François Arago (1786-1853), Henry Kater (1777-1835 ). Friedrich Wilhelm Bessel (1784-1846) led to a he designed and produced by Johann Georg Repsold pendulum apparatus by extensive studies on the pendulum length and the factors influencing them.