In the world around us, there are many phenomena and processes that, by and large, are invisible, not because they do not exist, but because we simply do not notice them. They are always present and are the same imperceptible and obligatory essence of things, without which it is difficult to imagine our life. Everyone, for example, knows what an oscillation is: in its most general form, it is a deviation from the state of equilibrium. Well, well, the top of the Ostankino tower deviated by its own 5 meters, but what next? Will it freeze? Nothing of the kind, it will begin to come back, the equilibrium state will slip through and will deviate in the other direction, and so forever, until it exists. But tell me, many people really saw these quite serious fluctuations of such a huge structure? Everyone knows, hesitates, here and there, here and there, day and night, winter and summer, but somehow ... not noticeable. The reasons for the oscillatory process is another question, but its presence is an inseparable sign of everything.
Everything around hesitates: buildings, structures, clock pendulums, leaves on trees, violin strings, ocean surface, tuning fork legs ... Among the vibrations are chaotic, which do not have strict repeatability, and cyclic, in which the oscillating body undergoes a complete set of its changes, and then this cycle repeats exactly, generally speaking, infinitely long. Typically, these changes imply a sequential search of spatial coordinates, as can be seen in the example of oscillations of a pendulum or the same tower.
The number of oscillations per unit time is called the frequency F = 1 / T. The unit of frequency is Hz = 1 / s. It is clear that the cyclic frequency is a parameter of the oscillations of the same name of any kind. Nevertheless, in practice, this concept is accepted, with some additions, attributed mainly to rotational vibrations. It so happened in 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 parameters of movement. Based on this, rotational displacement is measured by angular units, i.e. one revolution is equal to 2π radians, and the cyclic frequency ῳ = 2π / T. From this expression one can easily see 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 quite so. The 2π and 2πF factors 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 resonant frequency formula, for example, is reduced by two factors. If the unit “rev / sec” is used in the calculations, the angular, cyclic, frequency ῳ numerically coincides with the value of the frequency F.
Oscillations, as the essence and form of existence of matter, and its material embodiment - the objects of our being, are of great importance in human life. Knowledge of the laws of oscillations allowed the creation of modern electronics, electrical engineering, and many modern machines. Unfortunately, fluctuations do not always bring a positive effect, sometimes they bring grief and destruction. Unaccounted oscillations, 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 a working state is the main task of many engineering applications, and the examination of industrial objects and mechanisms for vibration resistance is an essential element of maintenance.