Cyclic frequency - what and how?

In the world around us, there are many phenomena and processes that, by and large, are not noticeable, not because they are not there, 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 the most general form is a deviation from the state of equilibrium. Well, well, the top of the Ostankino tower has deviated to its 5 m, and what's next? So it will freeze? Nothing of the kind, will start to return back, slip the state of equilibrium 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 causes of the oscillatory process are another matter, but its presence is an inseparable sign of everything.

Everything is shaken around: buildings, structures, pendulums of the clock, leaves in the trees, violin strings, the surface of the ocean, the legs of the tuning fork ... Among the oscillations there are chaotic ones that do not have strict repeatability, and cyclic ones, in which for a time period T the vibrating body passes a full set of its Changes, 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 called the frequency 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 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, the rotational displacement is measured by angular units, i.e. One revolution is 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 resonant frequency, for example, is reduced by two factors. In the case of using the unit "rev / sec" in the calculations, the angular, cyclic, frequency ῳ numerically coincides with the value of the frequency F.

Oscillations, as the essence and form of the existence of matter, and its material embodiment - objects of our being, are of great importance in human life. Knowledge of the laws of oscillation allowed the creation of 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 the inspection of industrial facilities and mechanisms for vibration resistance is an indispensable element of maintenance.