Learning the pendulum - the frequency of oscillation

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parameters of oscillatory processes are well-known physical concepts - the amplitude and period.At the same time, by fluctuations understand the iterative process of periodic law changes in a physical quantity about its mean or zero.Let's say that this law has a sinusoidal character.So, if the function of F (x) is expressed by the form F (x) = K * sin (x), we have just such an oscillating function, which, remember, up and down, up and down ...

take onchart a specified function, in principle, any, value on the axis Y, y1 denote it, and moving along the X, find the next point y2 with a value of y1.If now for the X, from the point v2 defer interval equal to T = (y2 - y1), we get the point v3 and will be equal to Y1 and Y2.The shape of the graph between the two points exactly repeated in all subsequent intervals equal to T. Thus, we found a parameter T for the process described by the formula F (x) = K * sin (x), which has a remarkable property: the argument X to withinT to alter the function F (x) over the entire range of its values.Since changes in the X-axis unlimited time, in other words, the number of cycles T indefinitely lot, have a cyclic, i.e.I repeat, you change the function.Cycle T called the period of oscillation and is measured in seconds.But the technique is more common to use a unit of measurement known as the oscillation frequency, denoted f and the calculated f = 1 / T, a unit it is called hertz (Hz).The frequency of 1 Hz - is one oscillation per second.

We are surrounded by "staggering" the world.Fluctuations - it sounds, the electric current in the wires, vibration mechanism, the light, the tides, the rotation of the planets and ... do not count them among, these fluctuations.All of them have a fairly conventional boundaries of their frequency, say "a fluctuation range."For example, the oscillation frequency of human hearing frequencies sound - from 16 Hz to 20 kHz (1 kHz = 1000 Hz) and the frequency range of sounds spoken language lies in the range 100 - 4000 Hz.A well-known fact that not all people hear the full range of sounds - for many 12-15 kHz already within earshot.The technique applies the ultrasonic vibrations 100, 200 kHz and above.Details of the mechanism may vary in a wide range of frequencies - and share Hz, and tens of kHz.But most have a wide range of electromagnetic waves - from shares and to many thousand million Hz.In this section of the global spectrum of light waves is quite small, but that they are perceived by our organs of vision.Different oscillation frequency in the spectrum of light waves determines the color of visible light - from red to violet.

But back to "square one."Very often, it is convenient to use a slightly modified units.This workaround can simplify many formulas and make them more visible.And this is due to the fact that the sinusoidal oscillation functions suggests the possibility to use variables in units of measurement of angles - radians or degrees.But at the same time, in the calculation of "creeps" constant 2π, which, together with the frequency found in many mathematical expressions.Then they decided to introduce a modified unit of frequency measurement and gave it the name "cyclic frequency of oscillation."The essence of this unit is that its frequency is determined by the number of oscillations during the 2 * π seconds, ie,6.28 sec.Cyclic rate calculated by the formula ω = 2 * π * f.Belonging to the cyclic frequency is expressed by its unit of measurement - radians per second.

oscillatory system has still some parameters that characterize her personality.Take our good old pendulum and slightly solemn, give it to the state of the oscillatory process - tick-tock, tick-tock.It's enough to push him once and ... left alone.What will we see?A pendulum oscillates long enough without further application of force, its oscillation frequency does not change, and the amplitude decreases gradually, because of friction forces in the actual devices.Such fluctuations, when, after initiating a push motion of a pendulum or any other oscillating system, is determined only by its parameters, called his own.If we assume that while stopping power is zero, and it is quite simple - everything is in our hands, such a pendulum, it is a mathematical, it will oscillate forever, and the period of oscillation can be calculated from the known, which has already become a classic, the formula - C = 2* π * √ l / g.

From its analysis we can draw an important conclusion: the natural frequency of the pendulum is determined only by the internal parameters of the system - the length of the thread and the magnitude of the acceleration of Earth's gravity.