oscillatory processes - an important element of modern science and technology, so they always paid attention to the study as one of the "eternal" problems.The task of any knowledge - not mere curiosity, and its use in everyday life.And for this, and every day there are new technical systems and equipment.They are on the move, showing its essence, doing some work, or being fixed, retain the potential under certain conditions, to move to a state of motion.What is a movement?Without going into the jungle, we take the simplest interpretation: the material change in the position of the body relative to any coordinate system, which is conventionally considered fixed.
Among the huge number of options for movement of particular interest is oscillating, which is characterized in that the system repeats the change of its origin (or of physical quantities) at regular intervals - loops.Such fluctuations are called periodic or cyclic.Among them are a separate class of harmonic oscillations whose characteristic features (speed, acceleration, position in space, etc.) vary in time harmonically, iehaving a sinusoidal appearance.A remarkable property of the harmonic oscillations is that their combination is any other options, includingand non-harmonic.A very important concept in physics is the "phase of the oscillation," which means fixing the position of the oscillating body at a time.Measured phase in corner units - radians rather arbitrary, just as a convenient way to explain the periodic processes.In other words, the phase value defines the current state of the vibrational system.It could not be - because the phase fluctuations is the argument of a function that describes these fluctuations.The true value of the phase of the oscillatory motion of nature can mean coordinates, speed and other physical parameters varies harmonically, but common to them is the time dependence.
demonstrate that this phase of the oscillation is not difficult - it would require a simple mechanical system - the thread length r, and suspended her "material point" - sinker.We fix the thread in the center of the rectangular coordinate system and force our "pendulum" cool.Assume that it is willing to make an angular velocity w.Then, during the time t the rotation angle of the load will be φ = wt.Additionally, this expression should be considered the initial phase of the oscillations in the form of angle φ0 - the system state before driving.Thus, the total angle of rotation, the phase is calculated from the ratio of φ = wt + φ0.Then the expression for the harmonic function, and a projection of the coordinates of the load on the X-axis, we can write:
x = A * cos (wt + φ0), where A - amplitude of fluctuations in our case is equal to r - radius of the filament.
Similarly, the same projection on the Y-axis is written as follows:
y = A * sin (wt + φ0).
should be understood that the phase of the oscillation means in this case does not measure rotation "angle", and the angular measure of the time which expresses time in terms of angle.During this time, the load is rotated by a certain angle, which can be uniquely determined based on the fact that the angular velocity of the cyclic fluctuations w = 2 * π / T, where T - oscillation period.Therefore, if one period corresponds to the rotation by 2π radians, the part of the period, the time can be proportional to the angle expressed as a fraction of a full rotation of 2π.
fluctuations do not exist by themselves - sound, light, vibration is always the superposition, superposition of a large number of oscillations from different sources.Of course, the result of superposition of two or more vibrations affect their options, includingand the phase of the oscillation.Formula resultant oscillation, usually non-harmonic, thus can have a very complicated form, but this is just getting interesting.As discussed above, any non-harmonic oscillation can be represented as a large number of harmonic of the same amplitude, frequency and phase.In mathematics, this operation is called "in the expansion of a number" and is widely used in the calculations, such as strength of structures and facilities.The basis for these calculations is the study of harmonic oscillations with all the parameters, including phase.
