Pendulum

Simple gravity pendulum

EastHanSeismograph

Foucault pendulum animated

Howard astronomical regulator clock

BanjoPendulum

Shortt Synchronome free pendulum clock

Pendulum

A pendulum is a weight suspended from a pivot so that it can swing freely. 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 acting on the pendulum's mass causes it to oscillate about the equilibrium position, swinging back and forth. The time it takes for one complete cycle, a left swing and a right swing, is called the pendulum's period. The period depends on the length of the pendulum and to a slight degree on the amplitude, the width of the pendulum's swing.

History

The use of pendulums for timekeeping dates back to the 17th century when Galileo Galilei first proposed their use for this purpose. The first practical pendulum clock was developed by Christiaan Huygens in 1656, significantly increasing the accuracy of timekeeping. Pendulums were used extensively in clocks until the early 20th century when they were replaced by more accurate and less maintenance-intensive quartz and atomic oscillators.

Physics

The motion of a pendulum is a classic example of Simple Harmonic Motion (SHM) when disregarding non-linear effects. In the ideal case, the period T of a simple pendulum, which is the time taken for one complete cycle, is given by:

\[T = 2\pi\sqrt{\frac{L}{g}}\]

where L is the length of the pendulum and g is the acceleration due to gravity.

For small amplitudes, the period of swing is approximately the same for different size swings: that is, the period is isochronous. This property, called isochronism, was discovered by Galileo.

Types of Pendulums

There are several types of pendulums including the simple pendulum mentioned above, the compound pendulum or physical pendulum, the Foucault pendulum which demonstrates the Earth's rotation, and the Kater's pendulum used to measure the value of gravitational acceleration accurately.

Applications

Beyond timekeeping, pendulums have been employed in various scientific instruments, such as the gravimeter, which measures the acceleration of gravity, and in seismometers to detect and measure earthquakes. The Foucault pendulum, in particular, provides simple proof of the Earth's rotation.

Cultural Impact

Pendulums have also had a significant impact culturally and have been used in practices such as divination and hypnosis. Their predictable, rhythmic motion continues to fascinate and find new applications in art and science.