Oscillation
One Oscillation (also Oscillation) one designates the process Change in status, with the one mechanical or not-mechanical after one Disturbance/Deflection by an effect moving in opposite directions again into that Starting situation one brings. Except the temporal change of deflection thereby also different sizes swing: Speed and energy.
This change in status can periodically run; then the starting situation is periodically again reached. One can formulate it also still more general: One Oscillation is one as a function of that defines.
In this connection mechanical, electrical or also hydraulic can to be regarded:
- Mechanical variables of state: Elongation (deflection), Swinging speed, Swinging acceleration, Angle of rotation, Angular speed, Angular acceleration, , Moment
- Electrical variables of state: , , , , , ,
- Hydraulic variables of state: Flow rate (Delivered flow), Pressure, , Mass density, Head (Hoisting depth)
In the context of the opinion here those becomes harmonious oscillation as an important special case regards:
 with a harmonious oscillation. |
The picture on the right side shows an undamped harmonious oscillation with that Elongation (swinging way) <math>y(t)</math>, that <math>y_0</math> and that Period duration <math>T</math>.
The elongation <math>y(t)</math> at one time <math>t</math> the momentary, the amplitude the maximally possible value gives to the size <math>y</math> on. Those Period (physics) or those Oscillation duration is those exactly one oscillation period goes through, D. h. after that it again in the same schwingungszustand is. That the period duration T is those f, thus:<math>T = {1 \over f} \quad</math>.
A further designation form that is <math>\nu</math> (speak: "nue") and of them cycles per second.
An oscillation is harmonious, if those Resetting size (z.B. the resetting and
With
- <math>
\varphi (t) = 2 \pi f t+\varphi_0 </math> becomes those (entire)Phase designated, and f or <math>\nu</math> is those the oscillation.
The <math>2\pi</math> subject of the frequency, <math>\omega = 2\pi \cdot f</math>, is those Rotative frequency the oscillation.
Distinctions
One differentiates:
- absorbed and undamped Oscillations,
- free, forced (or independently excited), excited and parameter-excited Oscillations,
- linear and nonlinear Oscillations,
- Oscillations with a degree of freedom, with finally many degrees of freedom and with infinitely many degrees of freedom (continuous oscillators).
All these characteristics can be combined.
Absorbed one and undamped oscillations
 with a free absorbed oscillation. |
Actual physical systems are always absorbed, there them, z. B. through to the environment. If one leaves oneself such a system (free oscillation), then this leads finally to the "stop", as from that comes out. are thus (already because of of the Principle of conservation of energy) not possible.
In the case of a free absorbed oscillation the reduction of the amplitude is by those Absorption size determined. In the reality the daempfungskraft is frequently proportional to the speed (linear system) (generally: too <math>\dot{y}(t)</math>, the first temporal derivative of <math>y(t)</math>). In this case the amplitude takes off, D.h. those Envelope is an exponential curve. The picture on the right side shows the course of such an absorbed oscillation. An example of speed-proportional friction is the friction in one ( or , Staffs, Plates and Flat one.
Further examples
Typical everyday life examples of oscillations are simple Thread pendulum, the oscillation of the quartz crystal in the quartz clock, swings on a swing, uvm. But also the atoms in a crystal lattice swing around an equilibrium position. In addition, the change of the seasons, the turn of the earth, the heart impact or the movement of the sheets in the wind are strictly speaking oscillations. Here there are everywhere temporal changes of variables of state.
An oscillation of the thread pendulum begins with the fact that in the equilibrium body present an energy supplies itself (z.B. by deflection of the pendelmasse of a thread pendulum, D.h. Supply of potential energy). In principle also an initial speed (kinetic energy) can be supplied to the pendulum.
Those sucked. move-rubbing strength is here those pulls downward. Again arrived in the initial equilibrium position, is the entire supplied potential converted into kinetic energy, the pendulum moves by the equilibrium position through and reaches in the ideal case of non-existent friction again the same height. Equilibrium adjusts itself if the system minimized its potential energy.
That Thread pendulum one leads only in the border line of very low amplitudes harmonious oscillation out. If deflections become larger, then the resetting strength will grow not proportionally to deflection. This is thus an example of a nonlinear system, which behaves for small deflections however approximately like a linear system.
Oscillations can be affected however also at the same time by several forces, or a body knows several oscillations at the same time, D. h. implement overlaid. One can divide any movement of a body in the area into from each other independent directions of motion. That is, a body can be moved into the three directions in space (it to stand perpendicularly to each other), and turn still around three thought movement axles (they stand likewise one on the other perpendicularly). Thus each rigid body in the area has six freedom of movement degrees.
The developing overlapping figures become after their discoverer LissajousLoops mentioned.
Web on the left of
