Oscillation is a repetitive or periodic variation, typically in time, of some measure about a central value or between two or more different states. It is the process of repeating variations of any quantity or measure about its equilibrium value in time. Oscillations can be used in physics to approximate complex interactions, such as those between atoms. Oscillations occur not only in mechanical systems but also in dynamic systems in virtually every area of science, such as the beating of the human heart, business cycles in economics, predator-prey population cycles in ecology, geothermal geysers in geology, vibration of strings in guitar and other string instruments, periodic firing of nerve cells in the brain, and the periodic swelling of Cepheid variable stars in astronomy.
Objects that show motion around an equilibrium point are known as oscillators. The most common examples of oscillation are the tides in the sea and the movement of a simple pendulum in a clock. Another example of oscillation is the movement of spring. The vibration of strings in guitars and other string instruments are also examples of oscillations. A sine wave is a perfect example of oscillation. Here, the wave moves between two points about a central value. The height or the maximum distance that the oscillation takes place is called the amplitude, and the time taken to complete one complete cycle is called the time period of the oscillation. Frequency is the number of complete cycles that occur in a second.
The mathematics of oscillation deals with the quantification of the amount that a sequence or function tends to move between extremes. There are several related notions: oscillation of a sequence of real numbers, oscillation of a real-valued function at a point, and so on.
