Oscillatory processes are an important element of modern science and technology, therefore their study has always been given attention as one of the “eternal” problems. The task of any knowledge is not mere curiosity, but its use in everyday life. And for this, new technical systems and mechanisms exist and appear daily. They are in motion, manifest their essence, performing some kind of work, or, being motionless, retain the potential possibility under certain conditions to go into a state of motion. And what is movement? Without delving into the jungle, we accept the simplest interpretation: a change in the position of a material body relative to any coordinate system that is conventionally considered motionless.
Among the huge number of possible variants of motion, of particular interest is the oscillatory one, which is distinguished by the fact that the system repeats a change in its coordinates (or physical quantities) at certain intervals of time - cycles. Such oscillations are called periodic or cyclic. Among them, harmonic vibrations are distinguished as a separate class , in which characteristic features (speed, acceleration, position in space, etc.) change in time according to a harmonic law, i.e. having a sinusoidal appearance. A remarkable property of harmonic oscillations is that their combination represents any other options, including and inharmonious. A very important concept in physics is the “phase of oscillations”, which means fixing the position of the oscillating body at some point in time. The phase is measured in angular units - radians, rather arbitrarily, simply as a convenient technique for explaining periodic processes. In other words, the phase determines the value of the current state of the oscillatory system. It cannot be otherwise - after all, the phase of oscillations is an argument of the function that describes these oscillations. The true value of the phase for the motion of an oscillatory nature can mean coordinates, speed, and other physical parameters that vary in harmonic law, but the time dependence is common to them.
It is not at all difficult to demonstrate what the oscillation phase is - it will require a simple mechanical system — a thread of length r, and a “material point” suspended on it — a weight. We fix the thread in the center of the rectangular coordinate system and make our “pendulum” spin. Suppose that he willingly does this with an angular velocity w. Then, over time t, the rotation angle of the load will be φ = wt. Additionally, in this expression, the initial phase of oscillations in the form of angle φ0, the position of the system before the start of motion, should be taken into account. So, the full angle of rotation, phase, is calculated from the relation φ = wt + φ0. Then the expression for the harmonic function, and this is the projection of the load coordinate on the X axis, can be written:
x = A * cos (wt + φ0), where A is the oscillation amplitude, in our case, equal to r - the radius of the thread.
Similarly, the same projection onto the Y axis can be written as follows:
y = A * sin (wt + φ0).
It should be understood that the phase of the oscillations in this case does not mean a measure of rotation “angle”, but an angular measure of time, which expresses time in units of angle. During this time, the load rotates through a certain angle, which can be uniquely determined based on the fact that the angular velocity for cyclic oscillation is w = 2 * π / T, where T is the period of oscillation. Therefore, if a rotation by 2π radians corresponds to one period, then part of the period, time, can be proportionally expressed by the angle as a fraction of the total rotation 2π.
Oscillations do not exist on their own - sounds, light, vibration are always a superposition, superposition, a large number of vibrations from different sources. Of course, the result of superposition of two or more oscillations is influenced by their parameters, incl. and oscillation phase. The formula for the total fluctuation, as a rule, is not harmonic, and at the same time it can have a very complex form, but this only makes it more interesting. As mentioned above, any non-harmonic oscillation can be represented as a large number of harmonic oscillations with different amplitudes, frequencies, and phases. In mathematics, such an operation is called “expansion of a function in a series” and is widely used in calculations, for example, the strength of structures and structures. The basis of such calculations is the study of harmonic vibrations taking into account all parameters, including phase.