Pendulum

I

Introduction

Pendulum, device consisting of an object suspended from a fixed point that swings back and forth under the influence of gravity (see Gravitation). Pendulums are used in several kinds of mechanical devices; for example, certain types of clocks use pendulums (see Clocks and Watches).

The most basic type of pendulum is the simple pendulum. In a simple pendulum, which oscillates back and forth in a single plane, all the mass of the device can be considered to reside entirely in the suspended object. The motion of pendulums such as those in clocks closely approximates the motion of a simple pendulum. A spherical pendulum is not confined to a single plane, and as a result its motion can be much more complicated than the motion of a simple pendulum.

The principle of the pendulum was discovered by Italian physicist and astronomer Galileo, who established that the period for the back-and-forth oscillation of a pendulum of a given length remains the same, no matter how large its arc, or amplitude. (If the amplitude is too large, however, the period of the pendulum is dependent on the amplitude.) This phenomenon is called isochronism, and Galileo noted its possible applications in timekeeping. Because of the role played by gravity, however, the period of a pendulum is related to geographical location, because the strength of gravity varies as a function of latitude and elevation. For example, the period will be greater on a mountain than at sea level. Thus, the pendulum can be used to determine accurately the local acceleration of gravity.

II

Compensation Pendulum

The simple pendulum, used for timekeeping, is accurate as a regulator, if the proper length of the rod is preserved. It was found, however, that in winter clocks went too fast, and at midsummer too slow because cold shortened the metallic rod and heat lengthened it. A refinement was made to ensure uniform length and accurate timekeeping by the use of compensation pendulums. The two common types of compensation pendulum are the mercury pendulum and the gridiron pendulum. The mercury pendulum carries a glass cylinder almost full of mercury. When the pendulum expands downward because of heat, the change is counterbalanced by the upward expansion of the mercury in the cylinder. The gridiron pendulum is composed of a series of upright metal bars, usually of steel and copper, having different compositions and therefore different coefficients of thermal expansion. If the relative lengths of these bars are carefully adjusted, no change of temperature will affect the pendulum's timekeeping.

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III

Other Pendulums

Pendulums used in various types of scientific instruments include the bifilar pendulum, the Foucault pendulum, and the torsion pendulum. Bifilar pendulums employ two strings or wires, and they have been used to record the irregular rotation of the earth as well as to detect earthquakes. The Foucault pendulum, used to demonstrate the rotation of the earth, is named after French physicist Jean Bernard Leon Foucault. The pendulum consists of a heavy bob suspended on a long wire; Foucault used a 28-kg (62-lb) bob attached to a 67-m (220-ft) wire. After the pendulum is set in motion so that it swings back and forth in a single plane, the rotation of the earth causes the orientation of the back-and-forth motions of the pendulum to slowly rotate with respect to the ground underneath the pendulum. The effect is most pronounced at the North Pole, where the pendulum rotates once every 24 hours. The rate of the pendulum's rotation with respect to the ground decreases with latitude; at the equator the pendulum does not rotate at all.

A torsion pendulum consists of a wire or some other fiber. The pendulum oscillates by repeatedly twisting and untwisting about the axis through the center of the wire. Though it is not strictly a pendulum since it does not oscillate because of the force of gravity, the mathematical formulas that describe the motion of a torsion pendulum are similar to the equations that describe the motion of a simple pendulum. (See Torsion; Torsion Balance).

See Equilibrium.

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