We study the pendulum - the oscillation frequency

Parameters of oscillatory processes are well-known physical concepts - amplitude and period. In this case, oscillations are understood as the process of changing the physical quantity that is repeatedly repeated according to the periodic law near its mean or zero value. Let us assume that this law has a sinusoidal character. So, if the function function F (x) is expressed by a formula of the form F (x) = K * sin (x), then we have just such an oscillating function, which, remember, up and down, up and down ...

Take on the graph of the indicated function some, in principle, any value on the Y axis, denote it by y1, and, moving along the X axis, we find the next point y2 with the value equal to y1. If we now plot the segment equal to T = (y2 - y1) along the X axis from the point y2, then we get the point y3 and it will be equal to y1 and y2. The shape of the graph between these points is exactly repeated on all subsequent segments equal to T. Thus, we found a certain parameter T for the process described by the formula F (x) = K * sin (x), which has a remarkable property: changes in the argument X within T lead to a change in the function F (x) over the whole range of its values. Since the changes along the X axis are unlimited in time, in other words, the number of cycles T is infinitely large, then we have a cyclic one, i.e. Repeated, change of function. The cycle duration T is called the oscillation period and is measured in seconds. But in engineering it is more common to use a unit of measurement, which is called the frequency of oscillations, is denoted by f and is calculated by f = 1 / T, and its unit of measure is called Hertz (Hz). The frequency of 1 Hz is one oscillation per second.

We are surrounded by a "wavering" world. Oscillations are sounds, the electric current in the wires, the vibrations of the mechanisms, the light, the ebbs and tides, the rotation of the planets and ... do not consider them numbers, these vibrations. All of them have rather conventional boundaries of their frequencies, they say "their own range of oscillations". Thus, for example, the frequency of vibrations of audible sound frequencies from 16 Hz to 20 kHz (1 kHz = 1000 Hz), and the frequency range of spoken language sounds is within the range of 100-4000 Hz. It is a well-known fact that not all people hear the whole range of sounds - for many 12-15 kHz there is already a limit of audibility. The technique employs ultrasonic vibrations of 100, 200 kHz and higher. The details of the mechanisms can also fluctuate in a large frequency range - and the fraction of Hz, and tens of kHz. But the most wide range have electromagnetic oscillations - from fractions and up to many thousands of millions of Hz. In this global spectrum, the area of light waves is very small, but it is our eyes that perceive them . The different frequency of oscillations in the spectrum of light waves determines the color of visible light - from red to violet.

However, we will return to "our own circles". Very often, it is convenient to use a few changed units of measure. Such an artificial device makes it possible to simplify many formulas and make them more visible. And this is due to the fact that the sinusoidal nature of the oscillatory functions assumes the possibility of using variables in units of angle measurements - radians or degrees. But at the same time, the "creeps" constant in the calculation is 2π, which, together with the frequency, is present in many mathematical expressions. Then they decided to introduce a modified unit of frequency and gave it the name "cyclic frequency of oscillations". The essence of this unit is that for it the frequency is determined by the number of oscillations in the time 2 * π seconds, i.e. 6.28 seconds The cyclic frequency is calculated by the formula ω = 2 * π * f. Membership to the cyclic frequency is expressed by its unit of measurement - radian per second.

The oscillatory system has some more parameters characterizing its individuality. Take our old, kind pendulum and, slightly solemnly, bring it into the state of the oscillatory process - tick-tock, tick-tock. To do this, it is enough to push it once and ... leave it alone. What will we see? The pendulum oscillates for a long time without additional force, its oscillation frequency does not change, and the amplitude gradually decreases, due to the presence of frictional forces in real devices. Such oscillations, when after an initializing impulse the motion of a pendulum, or any other oscillatory system, is determined only by its parameters, are called proper. If we assume that the stopping forces are equal to zero, and this is quite simple-everything is in our hands, then such a pendulum, called mathematical, will oscillate forever, and the period of oscillations can be calculated from the well-known, already classical, formula, T = 2 * Π * √ l / g.

From its analysis, one can draw an important conclusion: the natural frequency of oscillations of the pendulum is determined only by the internal parameters of the system-the length of the filament and the magnitude of the acceleration of the earth's gravitational force.