The parameters of the oscillatory processes are well-known physical concepts - amplitude and period. Moreover, by fluctuations we understand the process of changing a physical quantity that is repeatedly repeated according to a periodic law around its average or zero value. Assume that this law is sinusoidal in nature. So, if the function of the process F (x) is expressed by a formula of the form F (x) = K * sin (x), then we have just such an oscillating function, which, remember, up and down, up and down ...
We take on the graph of the indicated function some, in principle, any value along the Y axis, denote it by y1, and moving along the X axis, we find the next point y2 with a value equal to y1. If now on the X axis, from the point y2, to postpone a segment equal to T = (y2 - y1), then we get the point y3 and it will be equal to y1 and y2. The shape of the graph between these points repeats exactly on all subsequent segments equal to T. Thus, we found a certain parameter T for the process described by the formula F (x) = K * sin (x), which has a remarkable property: changes in the argument X within T lead to a change in the function F (x) in the entire range of its values. Since the changes along the X axis are unlimited in time, in other words, the number of cycles T is unlimited, we have a cyclic one, i.e. repetitive, change in function. The duration of the cycle T is called the oscillation period and is measured in seconds. But in technology it is more common to use a unit of measurement, called the oscillation frequency, denoted by f and calculated f = 1 / T, and its unit of measurement is called hertz (Hz). A frequency of 1 Hz is one oscillation per second.
We are surrounded by an "oscillating" world. Oscillations are sounds, electric current in wires, vibration of mechanisms, light, ebbs and flows, rotation of planets and ... do not count them numbers, these vibrations. All of them have rather arbitrary boundaries of their frequencies, they say "their range of oscillations." So, for example, the oscillation frequency of sound frequencies heard by a person is from 16 Hz to 20 kHz (1 kHz = 1000 Hz), and the frequency range of the sounds of colloquial speech is in the range of 100 - 4000 Hz. It is a well-known fact that not all people hear the entire range of sounds - for many 12-15 kHz there is already a hearing limit. The technology uses ultrasonic vibrations of 100, 200 kHz and higher. Details of mechanisms can also fluctuate over a wide frequency range — both fractions of Hz and tens of kHz. But the widest range has electromagnetic oscillations - from fractions to many thousands of millions of Hz. In this global spectrum, the section of light waves is very small, but it is precisely these organs of vision that perceive them . The different frequency of oscillations in the spectrum of light waves determines the color of visible light - from red to purple.
However, let's return to our own circles. Very often, it turns out to be convenient to use slightly modified units. Such an artificial technique makes it possible to simplify many formulas and make them more visual. And this is due to the fact that the sinusoidal nature of the oscillatory functions suggests the ability to use variables in units of measurement of angles - radians or degrees. But at the same time, the constant 2π “creeps in” into the calculations, which, together with the frequency, is present in many mathematical expressions. Then they decided to introduce a modified unit of measurement of frequency and gave it the name “cyclic oscillation frequency”. The essence of this unit is that for it the frequency is determined by the number of oscillations in a time of 2 * π seconds, i.e. 6.28 sec The cyclic frequency is calculated by the formula ω = 2 * π * f. Belonging to a cyclic frequency is expressed by its unit of measure - radian per second.
The oscillatory system has some more parameters characterizing its individuality. Take our old, good pendulum and, slightly solemnly, bring it into a state of oscillatory process - tick-tock, tick-tock. To do this, just push it once and ... leave it alone. What will we see? The pendulum oscillates for a long time without additional application of force, its oscillation frequency does not change, and the amplitude decreases gradually, due to the presence of friction forces in real devices. Such oscillations, when after the initializing push the movement of the pendulum, or any other oscillatory system, is determined only by its parameters, are called intrinsic. If we assume that in this case the stopping forces are equal to zero, and this is very simple - everything is in our hands, then such a pendulum, it is called mathematical, will oscillate forever, and the oscillation period can be calculated using the well-known, already classic, formula - T = 2 * π * √ l / g.
An important conclusion can be drawn from its analysis: the natural frequency of the oscillations of the pendulum is determined only by the internal parameters of the system — the length of the string and the magnitude of the acceleration of gravity.