We study oscillations - the phase of oscillations
Vibrational processes are an important elementmodern science and technology, so their attention has always been paid to attention as one of the "eternal" problems. The task of any knowledge is not just curiosity, but its use in everyday life. And for this, there are new technical systems and mechanisms that appear daily. They are in motion, manifest their essence, performing some work, or, being immobile, they retain the potential to change to a state of motion under certain conditions. And what is movement? Without delving into the jungle, we take the simplest interpretation: a change in the position of the material body with respect to any coordinate system that is conventionally considered stationary.
Among the huge number of possible optionsThe movement of particular interest is vibrational, which differs in that the system repeats the change in its coordinates (or physical quantities) at definite intervals of time-cycles. Such oscillations are called periodic or cyclic. Among them, harmonic oscillations are singled out as a separate class, in which the characteristic features (speed, acceleration, position in space, etc.) vary in time according to the harmonic law, i.e. having a sinusoidal form. A remarkable property of harmonic oscillations is that their combination represents any other options, including and nonharmonic. A very important concept in physics is the "phase of oscillations," which means fixing the position of an oscillating body at some point in time. The phase in angular units - radians is measured, it is rather conditional, just 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 can not be otherwise, because the phase of oscillations is the argument of a function that describes these oscillations. The true value of a phase for motion of an oscillatory character can mean coordinates, velocity, and other physical parameters that vary according to the harmonic law, but the time dependence is common for them.
Demonstrate what is the phase of oscillations,it is not difficult at all - this requires a simple mechanical system - a thread, a length r, and suspended on it "material point" - a weight. We fix the thread in the center of the rectangular coordinate system and make our "pendulum" spin. Let us assume that he willingly does this with the angular velocity w. Then, during the time t, the angle of rotation of the load is φ = wt. In addition, in this expression, the initial phase of oscillations in the form of an angle φ0 - the position of the system before the beginning of the movement should be taken into account. So, the total rotation angle, the phase, is calculated from the relation φ = wt + φ0. Then the expression for the harmonic function, and this is the projection of the coordinate of the load on the X axis, can be written:
x = A * cos (wt + φ0), where A is the amplitude of the oscillation, in our case equal to r - the radius of the filament.
Similarly, the same projection on the Y axis will be written as follows:
y = A * sin (wt + φ0).
It should be understood that the phase of oscillations means inIn this case, not the measure of rotation "angle", but the angular measure of time, which expresses time in units of angle. During this time, the cargo rotates through a certain angle, which can be uniquely determined, starting from the fact that the angular velocity for the cyclic vibration is w = 2 * π / T, where T is the oscillation period. Consequently, if one turn corresponds to a rotation of 2π radians, then a part of the period, time, can be proportional to the angle as a fraction of the total rotation 2π.
Oscillations do not exist by themselves - sounds,light, vibration are always superposition, overlap, a large number of oscillations from different sources. Of course, the result of imposing two or more oscillations is influenced by their parameters, incl. and the phase of oscillations. The formula for the total oscillation, as a rule, is non-harmonic, and can have a very complicated form, but this only makes it more interesting. As stated above, any nonharmonic vibration can be represented as a large number of harmonic oscillations with different amplitude, frequency, and phase. In mathematics, this operation is called "expansion of a function in a row" and is widely used in calculations, for example, the strength of structures and structures. The basis for such calculations is the study of harmonic oscillations taking into account all the parameters, including the phase.