# harmonic motion

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## harmonic motion,

regular vibration**vibration,**

in physics, commonly an oscillatory motion—a movement first in one direction and then back again in the opposite direction. It is exhibited, for example, by a swinging pendulum, by the prongs of a tuning fork that has been struck, or by the string of a musical

**.....**Click the link for more information. in which the acceleration

**acceleration,**

change in the velocity of a body with respect to time. Since velocity is a vector quantity, involving both magnitude and direction, acceleration is also a vector. In order to produce an acceleration, a force must be applied to the body.

**.....**Click the link for more information. of the vibrating object is directly proportional to the displacement of the object from its equilibrium

**equilibrium,**

state of balance. When a body or a system is in equilibrium, there is no net tendency to change. In mechanics, equilibrium has to do with the forces acting on a body.

**.....**Click the link for more information. position but oppositely directed. A single object vibrating in this manner is said to exhibit simple harmonic motion (SHM). More complex harmonic motion can be analyzed as combinations of two or more simple harmonic motions. Examples of objects whose motion approximates SHM are a pendulum

**pendulum,**

a mass, called a bob, suspended from a fixed point so that it can swing in an arc determined by its momentum and the force of gravity. The length of a pendulum is the distance from the point of suspension to the center of gravity of the bob (see center of mass).

**.....**Click the link for more information. swinging in a small arc, a mass bouncing at the end of a stretched spring, and air molecules vibrating back and forth as a sound

**sound,**

any disturbance that travels through an elastic medium such as air, ground, or water to be heard by the human ear. When a body vibrates, or moves back and forth (see vibration), the oscillation causes a periodic disturbance of the surrounding air or other medium that

**.....**Click the link for more information. wave passes. Simple harmonic motion is a periodic motion; that is, it repeats itself at regular intervals. The time required for one complete vibration of the object is the period of the motion. The inverse of the period is the frequency, which is the number of vibrations per unit of time. The maximum displacement of the object from its central position of equilibrium is the amplitude of the motion. At maximum displacement the velocity of the object is zero; the velocity is greatest when the object passes through its equilibrium position. These terms are commonly used to describe any periodic phenomenon, e.g., wave

**wave,**

in physics, the transfer of energy by the regular vibration, or oscillatory motion, either of some material medium or by the variation in magnitude of the field vectors of an electromagnetic field (see electromagnetic radiation).

**.....**Click the link for more information. motion and the rotation or revolution of an astronomical body. For any real harmonic motion, various forces act to reduce the amplitude with each vibration, i.e., to damp the motion. If these forces are small compared to the restoring force arising from the original displacement, then the object will vibrate a number of times with successively smaller amplitudes until the motion gradually dies out; this is known as damped harmonic motion. For a certain value of the damping forces, the object returns to its original position in a minimum amount of time and comes to rest at that position; such motion is termed critically damped. If the damping forces are large compared to the restoring force, the object returns slowly to its original position without vibrating at all; the system is said to be overdamped.

## Harmonic motion

A periodic motion that is a sinusoidal function of time. It is often called simple harmonic motion (SHM). It is the simplest possible type of vibratory motion. The motion is symmetric about its midpoint, at which the velocity is greatest and the acceleration is zero. At the extreme displacements or turning points, the velocity is zero, and the acceleration is a maximum. The motion is characterized by a unique frequency (without overtones).

Harmonic motion may be present in very simple mechanisms. For example, if a wheel is rotating at a constant speed about a fixed axis, the projection on any fixed line of the motion of a point on the wheel is simple harmonic. Harmonic motion may also result from the response of a vibrating system to a periodic—in particular a sinusoidal—force. Harmonic motion is the typical motion of most simple systems that have been displaced from a position of stable equilibrium and then released, provided that the damping is negligible. The motion of a pendulum is approximately simple harmonic for small amplitudes. *See* Pendulum

The realization that atoms are continually vibrating in motions that are nearly harmonic is essential for understanding many properties of matter, including molecular spectra, heat capacity, and heat conduction. *See* Damping, Forced oscillation, Harmonic oscillator, Lattice vibrations, Molecular structure and spectra, Periodic motion, Vibration, Wave motion

## harmonic motion

[här′män·ik ′mō·shən]*x*=

*a*cos (

*kt*+ θ), where

*t*is the time parameter, and

*a*,

*k*, and θ are constants. Also known as harmonic vibration; simple harmonic motion (SHM).