Kater's pendulum

A reversible pendulum is in gravimetry a pendulum to measure the acceleration of gravity. It has two adjustable points or agate - cutting for suspension and adjustment of the adjustable pendulum masses.

The peculiarity of Reversionspendeln is that the two suspension points are adjusted so that they have exactly the same oscillation period. Thus, the difficult question of determining the center of gravity of the pendulum to determine the pendulum length exactly.

This problem reduces to the measurement of the distance between the two cutting edges whose value is to be entered in the oscillation formula pendulum length.

With this method, it has already been before the turn of the century can determine the acceleration due to gravity at about one millionth of its value (see pendulum apparatus of Sterneck ). Developed in the mid- 20th century gravimeter according to the principle of the spring balance have reached this accuracy only by high costs for construction, calculation methods and reductions, but have become more accurate by a factor of 10 to 100.

After specifying multiple sources, the reversible pendulum of Johann Gottlieb Friedrich von beans Berger was invented. Outside the German-speaking countries, the term has largely prevailed cat pendant for the reversible pendulum, which refers to the construction of the British physicist Henry Kater in 1817.

Principle of operation

The figure shows the schematic structure of a reversible pendulum with two movable masses.

If the moment of inertia with respect to the center of gravity of the pendulum is valid according to Steiner's theorem for the moment of inertia with respect to the cutting edge at a distance from the centroid

The result for small deflections, the oscillation period

The same applies to.

You are now determined the positions of the masses so that the oscillation periods and are the same for oscillations around or is obtained with ( l: reduced pendulum length):

Analogous considerations apply to the reversible with adjustable cutting. Can you measure the distance between the blades and the oscillation period precisely, it can be precisely determined with this experiment, the local acceleration due to gravity, and thus the local factor.