oscillatory processes surround a person everywhere.This phenomenon is due to the fact that, firstly, in nature there are many media (physical, chemical, organic, etc.) under which oscillates including damped oscillations.Secondly, in the reality around us there is a huge variety of oscillating systems whose very existence is linked to the oscillatory processes.These processes are all around us, they characterize the flow of current in the wires, light phenomena, propagation and more.In the end, the man himself, or rather the human body is an oscillating system, whose life provided by different types of vibrations - the heartbeat, breathing, blood circulation, limb movement.
Therefore, they are studying various sciences, including interdisciplinary.Simple and original in this study were free oscillations.They are characterized by the exhaustion of the vibrational energy of the pulse, so they finally stopped, but because such fluctuations are determined by the concept of damped oscillations.
in oscillatory systems objectively the process of the loss of energy (mechanical systems - due to friction in the electric - because of electrical resistance).That is why such damped oscillations can not be classified as harmonic.Given this initial statement, we can express mathematically derived, for example, the mechanics of damped oscillations formula expresses so: F = - rV = -r dx / dt.In this formula, r is a coefficient of resistance constant.According to the formula, we can conclude that the value of the velocity (V) for a given system is proportional to the resistance value.But the presence of the sign "-" means that the force vector (F) and speed are multidirectional nature.
Applying equation Newton's second law, and taking into account the effect of the resistance forces, the equation characterizing the damped oscillations of movement, takes the following form: in the presence of the forces of resistance is given by: d ^ 2 / dt2 + 2β dt / dt + ω2 x = 0. InThe formula β - damping factor, which shows the intensity of this phase of the oscillation process.
Quite similar equation can be obtained for an electric circuit, taking into account the damping and added to the left side of the value of the voltage drop across the resistor UR.Only in this case, the differential equation is not recorded for the time offset (t), and to charge the capacitor q (t);the friction coefficient r is replaced by the electrical resistance of the chain R;2 wherein β = R / L, where: K - circuit resistance, L - the length of the chain.
If on the basis of formulas to construct the corresponding graphs, you can see that the graph of damped oscillations is very similar graphics harmonic oscillations, but the amplitude of the oscillations gradually decreases exponentially.
Given the fact that the oscillations may be performed by various oscillatory systems and occur in different environments, we should stipulate that, what kind of system we are considering in each case.From this condition depends not only on the flow characteristics of oscillatory processes, but going the opposite effect - the very nature of the oscillations is determined by the system and its classification place.We, in this case, considered one in which the properties of the system remain unchanged in the study of the oscillatory process.For example, we accept that the process does not change the spring tension, the force of gravity acting on the load, and electrical systems remain unchanged, depending on the resistance of the oscillating velocity or acceleration value.These are referred to as linear oscillating systems.
