# Oscillation - Real-life applications

Photo by: chrisharvey

### Springs and Damping

Elastic potential energy relates primarily to springs, but springs are a major part of everyday life. They can be found in everything from the shock-absorber assembly of a motor vehicle to the supports of a trampoline fabric, and in both cases, springs blunt the force of impact.

If one were to jump on a piece of trampoline fabric stretched across an ordinary table—one with no springs—the experience would not be much fun, because there would be little bounce. On the other hand, the elastic potential energy of the trampoline's springs ensures that anyone of normal weight who jumps on the trampoline is liable to bounce some distance into the air. As a person's body comes down onto the trampoline fabric, this stretches the fabric (itself highly elastic) and, hence, the springs. Pulled from a position of equilibrium, the springs acquire elastic potential energy, and this energy makes possible the upward bounce.

As a car goes over a bump, the spring in its shock-absorber assembly is compressed, but the elastic potential energy of the spring immediately forces it back to a position of equilibrium, thus ensuring that the bump is not felt throughout the entire vehicle. However, springs alone would make for a bouncy ride; hence, a modern vehicle also has shock absorbers. The shock absorber, a cylinder in which a piston pushes down on a quantity of oil, acts as a damper—that is, an inhibitor of the springs' oscillation.

#### SIMPLE HARMONIC MOTION AND DAMPING.

Simple harmonic motion occurs when a particle or object moves back and forth within a stable equilibrium position under the influence of a restoring force proportional to its displacement. In an ideal situation, where friction played no part, an object would continue to oscillate indefinitely.

Of course, objects in the real world do not experience perpetual oscillation; instead, most oscillating particles are subject to damping, or the dissipation of energy, primarily as a result of friction. In the earlier illustration of the spring suspended from a ceiling, if the string is pulled to a position of maximum displacement and then released, it will, of course, behave dramatically at first. Over time, however, its movements will become slower and slower, because of the damping effect of frictional forces.

#### HOW DAMPING WORKS.

When the spring is first released, most likely it will fly upward with so much kinetic energy that it will, quite literally, bounce off the ceiling. But with each transit within the position of equilibrium, the friction produced by contact between the metal spring and the air, and by contact between molecules within the spring itself, will gradually reduce the energy that gives it movement. In time, it will come to a stop.

If the damping effect is small, the amplitude will gradually decrease, as the object continues to oscillate, until eventually oscillation ceases. On the other hand, the object may be "overdamped," such that it completes only a few cycles before ceasing to oscillate altogether. In the spring illustration, overdamping would occur if one were to grab the spring on a downward cycle, then slowly let it go, such that it no longer bounced.

There is a type of damping less forceful than overdamping, but not so gradual as the slow dissipation of energy due to frictional forces alone. This is called critical damping. In a critically damped oscillator, the oscillating material is made to return to equilibrium as quickly as possible without oscillating. An example of a critically damped oscillator is the shock-absorber assembly described earlier.

Even without its shock absorbers, the springs in a car would be subject to some degree of damping that would eventually bring a halt to their oscillation; but because this damping is of a very gradual nature, their tendency is to continue oscillating more or less evenly. Over time, of course, the friction in the springs would wear down their energy and bring an end to their oscillation, but by then, the car would most likely have hit another bump. Therefore, it makes sense to apply critical damping to the oscillation of the springs by using shock absorbers.

### Bungee Cords and Rubber Bands

Many objects in daily life oscillate in a spring-like way, yet people do not commonly associate them with springs. For example, a rubber band, which behaves very much like a spring, possesses high elastic potential energy. It will oscillate when stretched from a position of stable equilibrium.

Rubber is composed of long, thin molecules called polymers, which are arranged side by side. The chemical bonds between the atoms in a polymer are flexible and tend to rotate, producing kinks and loops along the length of the molecule. The super-elastic polymers in rubber are called elastomers, and when a piece of rubber is pulled, the kinks and loops in the elastomers straighten.

The structure of rubber gives it a high degree of elastic potential energy, and in order to stretch rubber to maximum displacement, there is a powerful restoring force that must be overcome. This can be illustrated if a rubber band is attached to a ceiling, like the spring in the earlier example, and allowed to hang downward. If it is pulled down and released, it will behave much as the spring did.

The oscillation of a rubber band will be even more appreciable if a weight is attached to the "free" end—that is, the end hanging downward. This is equivalent, on a small scale, to a bungee jumper attached to a cord. The type of cord used for bungee jumping is highly elastic; otherwise, the sport would be even more dangerous than it already is. Because of the cord's elasticity, when the bungee jumper "reaches the end of his rope," he bounces back up. At a certain point, he begins to fall again, then bounces back up, and so on, oscillating until he reaches the point of stable equilibrium.

### The Pendulum

As noted earlier, a pendulum operates in much the same way as a swing; the difference between them is primarily one of purpose. A swing exists to give pleasure to a child, or a certain bittersweet pleasure to an adult reliving a childhood experience. A pendulum, on the other hand, is not for play; it performs the function of providing a reading, or measurement.

One type of pendulum is a metronome, which registers the tempo or speed of music. Housed in a hollow box shaped like a pyramid, a metronome consists of a pendulum attached to a sliding weight, with a fixed weight attached to the bottom end of the pendulum. It includes a number scale indicating the number of oscillations per minute, and by moving the upper weight, one can change the beat to be indicated.

#### ZHANG HENG'S SEISMO-SCOPE.

Metronomes were developed in the early nineteenth century, but, by then, the concept of a pendulum was already old. In the second century A.D. , Chinese mathematician and astronomer Zhang Heng (78-139) used a pendulum to develop the world's first seismoscope, an instrument for measuring motion on Earth's surface as a result of earthquakes.

Zhang Heng's seismoscope, which he unveiled in 132 A.D. , consisted of a cylinder surrounded by bronze dragons with frogs (also made of bronze) beneath. When the earth shook, a ball would drop from a dragon's mouth into that of a frog, making a noise. The number of balls released, and the direction in which they fell, indicated the magnitude and location of the seismic disruption.

#### CLOCKS, SCIENTIFIC INSTRUMENTS, AND "FAX MACHINE".

In 718 A.D. , during a period of intellectual flowering that attended the early T'ang Dynasty (618-907), a Buddhist monk named I-hsing and a military engineer named Liang Ling-tsan built an astronomical clock using a pendulum. Many clocks today—for example, the stately and imposing "grandfather clock" found in some homes—like-wise, use a pendulum to mark time.

Physicists of the early modern era used pendula (the plural of pendulum) for a number of interesting purposes, including calculations regarding gravitational force. Experiments with pendula by Galileo Galilei (1564-1642) led to the creation of the mechanical pendulum clock—the grandfather clock, that is—by distinguished Dutch physicist and astronomer Christiaan Huygens (1629-1695).

In the nineteenth century, A Scottish inventor named Alexander Bain (1810-1877) even used a pendulum to create the first "fax machine." Using matching pendulum transmitters and receivers that sent and received electrical impulses, he created a crude device that, at the time, seemed to have little practical purpose. In fact, Bain's "fax machine," invented in 1840, was more than a century ahead of its time.

#### THE FOUCAULT PENDULUM.

By far the most important experiments with pendula during the nineteenth century, however, were those of the French physicist Jean Bernard Leon Foucault (1819-1868). Swinging a heavy iron ball from a wire more than 200 ft (61 m) in length, he was able to demonstrate that Earth rotates on its axis.

Foucault conducted his famous demonstration in the Panthéon, a large domed building in Paris named after the ancient Pantheon of Rome. He arranged to have sand placed on the floor of the Panthéon, and placed a pin on the bottom of the iron ball, so that it would mark the sand as the pendulum moved. A pendulum in oscillation maintains its orientation, yet the Foucault pendulum (as it came to be called) seemed to be shifting continually toward the right, as indicated by the marks in the sand.

The confusion related to reference point: since Earth's rotation is not something that can be perceived with the senses, it was natural to assume that the pendulum itself was changing orientation—or rather, that only the pendulum was moving. In fact, the path of Foucault's pendulum did not vary nearly as much as it seemed. Earth itself was moving beneath the pendulum, providing an additional force which caused the pendulum's plane of oscillation to rotate.

Brynie, Faith Hickman. Six-Minute Science Experiments. Illustrated by Kim Whittingham. New York: Sterling Publishing Company, 1996.

Ehrlich, Robert. Turning the World Inside Out, and 174 Other Simple Physics Demonstrations. Princeton, N.J.: Princeton University Press, 1990.

"Foucault Pendulum" Smithsonian Institution FAQs (Website). <http://www.si.edu/resource/faq/nmah/pendulum.html> (April 23, 2001).

Kruszelnicki, Karl S. The Foucault Pendulum (Web site). <http://www.abc.net.au/surf/pendulum/pendulum.html> (April 23, 2001).

Schaefer, Lola M. Back and Forth. Edited by Gail Saunders-Smith; P. W. Hammer, consultant. Mankato, MN: Pebble Books, 2000.

Shirley, Jean. Galileo. Illustrated by Raymond Renard. St. Louis: McGraw-Hill, 1967.

Suplee, Curt. Everyday Science Explained. Washington, D.C.: National Geographic Society, 1996.

Topp, Patricia. This Strange Quantum World and You. Nevada City, CA: Blue Dolphin, 1999.

Zubrowski, Bernie. Making Waves: Finding Out About Rhythmic Motion. Illustrated by Roy Doty. New York: Morrow Junior Books, 1994.