Simple harmonic motion
Simple harmonic motion (SHM) is a fundamental concept in physics that describes the repetitive back-and-forth movement of an object around a central point, or equilibrium position. This motion occurs when the displacement in one direction is equal to that in the opposite direction, exemplified by a pendulum or a weight on a spring. The term "harmonic" relates to the vibrations produced in musical instruments, which are similar to the oscillatory movements in SHM that create sound waves.
One key characteristic of SHM is that the oscillation will continue indefinitely unless interrupted by external forces or energy loss, such as friction. In practical scenarios, friction leads to damping, causing the oscillating object to gradually lose energy and slow down until it comes to rest. The effects of damping can be observed in everyday situations, such as with an automobile's suspension system, which utilizes springs to absorb jolts while preventing excessive oscillation.
The study of simple harmonic motion has wide-ranging applications, including demonstrations of physical principles like the Earth's rotation, as famously illustrated by the Foucault pendulum. Overall, SHM is a crucial concept that bridges various fields of science and illustrates fundamental principles of motion and energy transfer.
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Simple harmonic motion
Simple harmonic motion is a concept that is chiefly relevant in physics. It refers to an object moving repetitively, back and forth, in a medium, such that its displacement (i.e., movement away from the center) in one direction is equal to its displacement in the other direction. Essentially, the term describes the movement of a pendulum swinging back and forth, so that it swings the same distance to the left as it swings to the right. The same effect can be found when a weight is suspended from a spring: When the weight is at rest, the system is stable and does not move, but if the weight is pushed or pulled downward, it begins to exhibit simple harmonic motion—it travels upward from its point of equilibrium the same distance that it was pulled or pushed downward.
Background
The use of the term “harmonic” stems from the fact that the vibrations that musical instruments make in order to produce sound are of the same character. When musicians strike gongs, tap drums, or blow on horns, they are actually using the instrument to create vibrations that travel through the air and are interpreted by listeners’ ears as sounds. These vibrations take the form of sound waves, which cause particles in the medium (typically, the air) to vibrate back and forth in a wave pattern. Thus, because the motion in question produces musical harmony, the physical phenomenon has been dubbed simple harmonic motion.
Overview
One of the qualities of simple harmonic motion as physicists describe it is that the oscillation (the back-and-forth movement) will continue once it has been initiated, unless either something interferes with the oscillation or the system experiences energy loss. The oscillation can carry on indefinitely only in a vacuum. In the ordinary world, the oscillation will gradually decrease because of friction, as the oscillating object would encounter resistance from molecules of oxygen, nitrogen, carbon dioxide, and other trace materials in the air. The resistance will cause the object to slow down slightly as it travels to and from the central point of equilibrium, so that with each cycle of movement, the object travels a shorter distance in both directions. The continuation of this behavior eventually brings the movement of the object to a halt, again resting motionlessly.
The operations involved in simple harmonic motion do not depend on the mass of the object that is moving; the object could be a bowling ball or a particle, but the behavior would remain the same. The only difference would relate to the influence of external forces on the simple harmonic motion. To use the example of friction, a bowling ball has more surface area to bump into molecules from the air than a particle does, so the larger object would slow down before the smaller one, but the difference would not be due to any quality that is part of simple harmonic motion.
The gradual slowing down seen with simple harmonic motion under conditions where friction is present is known as “damping.” The process involves some of the energy in the simple harmonic motion system being removed from that system and transferred elsewhere, bit by bit. An example of this can be seen in an automobile’s suspension, which uses springs and shock absorbers to help reduce the jolting effect of driving over uneven surfaces. Driving over a bump compresses the spring, and the spring then begins to push back in the opposite direction, following the pattern of simple harmonic motion. Shock absorbers are then used to siphon energy out of the system—otherwise the back-and-forth motion of the spring would continue much longer than most passengers would find comfortable. Another example of damping is when one pushes a child on a swing. The child is first pulled backward, then swings forward when released almost as far as she had been pulled back. During each subsequent cycle, her momentum is dampened as it is used to push against the resistance of friction.
The study of simple harmonic motion has been of tremendous importance in a wide range of fields. One of the most famous is the Foucault pendulum, a relatively heavy pendulum observed by nineteenth-century scientist Jean Bernard Léon Foucault. Foucault used the motion of the pendulum to demonstrate that the earth rotates on its axis. He did this by setting up a pendulum over a floor covered with a smoothed layer of sand. He attached a pointer to the bottom of the pendulum, so that the pointer would trace a line in the sand as the pendulum swung. Since a pendulum that is oscillating keeps the same orientation (that is, it keeps swinging in the same space), observers expected to see the pointer on the pendulum trace the same line in the sand, over and over. Instead, they saw a series of lines, each one slightly to the right of the previous one. Since oscillating objects maintain their orientation, the pendulum was not swinging outside its arc, so the only other conclusion was that the earth was moving underneath the pendulum.
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"Simple Harmonic Motion." LibreTexts, 12 Sept. 2022, phys.libretexts.org/Bookshelves/University‗Physics/University‗Physics‗(OpenStax)/Book%3A‗University‗Physics‗I‗-‗Mechanics‗Sound‗Oscillations‗and‗Waves‗(OpenStax)/15%3A‗Oscillations/15.02%3A‗Simple‗Harmonic‗Motion. Accessed 21 Nov. 2024.