The physical world around us is filled with movement. It is almost impossible to find at least one physical body that could be considered as at rest. In addition to a uniformly translational rectilinear motion, motion along a complex path, motion with acceleration and others, we can observe firsthand or experience the influence of periodically repeated movements of material objects.
A man has long noticed the distinctive properties and features of oscillatory movements and even learned to use mechanical vibrations for his own purposes. All periodically repeated processes in time can be called oscillations. Mechanical vibrations are only a part of this diverse world of phenomena occurring according to almost the same laws. Using an illustrative example of mechanical repetitive movements, you can make basic rules and determine the laws by which electromagnetic, electromechanical, and other oscillatory processes occur.
The nature of the appearance of mechanical vibrations lies in the periodic transformation of potential energy into kinetic. An example of how energy is converted during mechanical vibrations can be described by examining a ball suspended from a spring. In a calm state, the force of gravity is balanced by the spring force of the spring. But it is worth taking the system out of equilibrium by force, thereby provoking movement from the side of the equilibrium point, as the potential energy begins its conversion into kinetic. And that, in turn, from the moment the ball passes the zero position will begin to be converted to potential. This process takes as long as the conditions for the existence of the system approach impeccable.
Oscillations occurring according to the law of sine or cosine are considered mathematically ideal. Such processes are commonly called harmonic vibrations. An ideal example of mechanical harmonic vibrations is the movement of a pendulum in an absolutely airless space when there is no influence of friction forces. But this is an absolutely flawless case, which is technically very difficult to achieve.
Mechanical vibrations, despite their duration, sooner or later cease, and the system occupies a position of relative equilibrium. This happens due to the waste of energy in overcoming the resistance of air, friction, and other factors that inevitably lead to the correction of calculations in the transition from ideal to real conditions in which the system in question exists.
Inevitably approaching deep study and analysis, we come to the need to mathematically describe mechanical vibrations. The formulas of this process include such quantities as amplitude (A), oscillation frequency (w), and initial phase (a). And the function of the dependence of the displacement (x) on time (t) in the classical form has the form
x = Acos (wt + a).
It is also worth mentioning the value characterizing mechanical vibrations, which has a name - period (T), which is mathematically determined as
T = 2Ο / w.
Mechanical vibrations, in addition to the descriptive description of the processes of oscillations of a non-mechanical nature, are of interest to us for some properties that, if used correctly, can have certain benefits, and if they are ignored, can lead to significant trouble.
Particular attention should be paid to the phenomenon of a sharp jump in amplitude during forced oscillations that occur when the frequency of the driving force approaches the frequency of the body's own vibrations. It is called resonance. Widely used in electronics, in mechanical systems, the resonance phenomenon is mainly destructive, it must be taken into account when creating a wide variety of mechanical structures and systems.
The next manifestation of mechanical vibrations is vibration. Its appearance can cause not only a certain discomfort, but also bring to the appearance of resonance. But, in addition to the negative impact, local vibration with a low intensity of manifestation can favorably affect the human body as a whole, improving the functional state of the central nervous system, and even accelerate wound healing , etc.
Among the manifestations of mechanical vibrations, one can distinguish the phenomenon of sound, ultrasound. The beneficial properties of these mechanical waves and other manifestations of mechanical vibrations are widely used in various fields of human life.