In the world around us, there are many phenomena andprocesses, which, by and large, are invisible not because they are not, but because we simply do not notice them. They are always present and are the same imperceptible and obligatory essence of things, without which our life is hard to imagine. Everyone, for example, knows that such an oscillation: in its most general form is a deviation from the state of equilibrium. Well, well, the top of the Ostankino tower strayed to its 5 m, and then what? So it will freeze? Nothing of the sort will start to go back, it will slip through the equilibrium state and will deviate to the other side, and so forever, as long as it exists. But tell me, did many people really see these quite serious fluctuations of such a huge structure? Everyone knows, hesitates, here-there, here-there, and day and night, winter and summer, but somehow ... not noticeable. The reasons for the oscillatory process are another matter, but its presence is an inseparable sign of everything.
Everything is moving around: buildings, structures, pendulums of the clock, leaves on trees, violin strings, the surface of the ocean, the legs of a tuning fork ... Among the oscillations there are chaotic ones that do not have a strict repeatability, and cyclic ones, in which the oscillating body passes a complete set of its changes over a period of time, and then this cycle repeats exactly, in general, infinitely long. Usually, these changes involve a sequential search of spatial coordinates, as can be observed in the case of oscillations of a pendulum or the same tower.
The number of oscillations per unit time is calledfrequency F = 1 / T. Unit of measurement of frequency - Hz = 1 / sec. It is clear that the cyclic frequency is a parameter of the same oscillations of any kind. Nevertheless, in practice, this concept, with some additions, is attributed primarily to fluctuations of a rotational nature. It so happened in the technology that rotational motion is the basis of most machines, mechanisms, devices. For such oscillations, one cycle is one revolution, and then it is more convenient to use the angular displacement parameters. Proceeding from this, rotational displacement is measured by angular units, i.e. one revolution is equal to 2π radians, and the cyclic frequency is ῳ = 2π / T. This relation easily shows the connection with the frequency F: ῳ = 2πF. This allows us to say that the cyclic frequency is the number of oscillations (full revolutions) in 2π seconds.
It would seem, not in the forehead, so ... Not exactly. The factors 2π and 2πF are used in many equations of electronics, mathematical and theoretical physics in sections where oscillatory processes are studied using the concept of cyclic frequency. The formula of the resonance frequency, for example, is reduced by two factors. In the case of using the unit "v / sec" in the calculations, the angular, cyclic, frequency ῳ numerically coincides with the value of the frequency F.
Oscillations, as essence and form of existencematter, and its material embodiment - objects of our being, are of great importance in human life. Knowledge of the laws of oscillation made it possible to create modern electronics, electrical engineering, many modern machines. Unfortunately, fluctuations do not always have a positive effect, sometimes they bring grief and destruction. Uncounted fluctuations, the cause of many accidents, cause premature aging of materials, and the cyclic frequency of resonant vibrations of bridges, dams, machine parts leads to their premature failure. The study of oscillatory processes, the ability to predict the behavior of natural and technical objects in order to prevent their destruction or exit from the working state is the main task of many engineering applications, and inspection of industrial facilities and mechanisms for vibration resistance is an indispensable element of maintenance.
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