Mechanical vibrations: what is it?

Time should be devoted to a short essay on oscillatory motion. But first you need to answer one important question. What is meant by mechanical vibrations? By them they mean movement, during which the observed body repeatedly occupies the same positions in space.

Physicists distinguish non-periodic and periodic oscillations. The first include those of which the coordinates and other characteristics of the body cannot be described using periodic functions of time. With the second view is easier. Periodic oscillations are those that can be described using periodic functions of time. But what do they mean by them? In physics, oscillations are also often understood as processes that repeat to a certain extent in time. And separately with respect to the topic under consideration, the following should be said. Mechanical oscillations can be conditionally classified as follows:

  1. Depending on the conditions of occurrence:
    1. Forced;
    2. Self-oscillation;
    3. Free
  2. Depending on the change in kinetic energy over time:
    1. Harmonic;
    2. Sawtooth;
    3. Fading.

mechanical vibrations

The article will consider not all, but only some types of vibrations. We should also mention the formulas, their use and diversity. In short, a lot of them. The variety in which mechanical vibrations are presented, formulas for determining their parameters, pushed scientists to create separate reference books designed for specific situations. To invent yourself, thus, nothing. When creating an oscillating system, it will only be necessary to spend half an hour or an hour to find a formula for a specific situation.

Characteristic of mechanical vibrations

mechanical energy conversion

Physical quantities are used to characterize mechanical vibrations, which provide the necessary data. The amplitude of oscillation is the largest deviation of the body, which swings from the initial value of the position. And what is the period? In it, vibrations are the time that the body needs to repeat all its movements, or in other words, it takes to perform one repetition of movement.What is meant by frequency? Under it understand the number equal to the number of oscillations made for one unit of time. Often in home, school and university experiments for the frequency of taking one second. Cyclic frequency is often used instead of the notion of the number of oscillations that occur per unit of time, and implies its calculation, which is necessary to perform one such cycle.

Harmonic mechanical vibrations

By harmonic oscillations are meant those of them whose physical quantity selected for the characteristic varies on a time interval in the form of a sinusoidal curve, which is easy to display in graphical mode. When the coordinate of the material point changes, according to the harmonic law, the impulse, speed and acceleration also change according to it.

Free oscillations

mechanical oscillations formula

When the oscillation is made in the system due to the initial energy, it is called free. As a practical display of this type of physical process, special models are used: the spring and mathematical pendulums. They allow you to work with the most common situations.As a mathematical pendulum, a point is taken that oscillates and hangs on an inextensible and weightless thread. There is no such device on earth. Therefore, the closest to the theoretical model is a structure composed of a ball, the diameter (size) of which is significantly smaller than the length of the thread. It is necessary to carry out physical actions. Deflect such a ball from its initial position and release. And so any experimenter will be able to see mechanical vibrations. The period, as well as their frequency, depend solely on the parameters of the system: the length of the thread of the mathematical pendulum, the spring stiffness, the mass of the load (important for the spring pendulum). Because of this, free oscillations are also called natural oscillations of the system. It is quite logical. And the frequency with which everything happens is called system.

mechanical vibrations

The transformation of energy during mechanical vibrations

Potential and kinetic energies during body movements transform into one another. And the same is the opposite. When the system deviates from the initial equilibrium position to the largest possible value, the potential energy also reaches its maximum value, while the kinetics of the body - the minimum. Separately, it should be said about one misconception, popular among people.When an equilibrium position is reached, the potential energy is at its minimum (it is usually considered that it is zero here), while the kinetics (and this is both the body momentum and the speed of its movement) reaches a maximum. In practice, something else is taken into account. In real systems, there are non-potential forces whose value does not equal zero. The energy of the system is wasted due to the work of the support forces, air friction, internal spring forces or suspension. The amplitude of the body oscillation gradually decreases. Such oscillations are called damped. If the force of friction is too large, then the entire energy supply can be used up within a period of one oscillation, and the movement of the body will not be periodic.

Forced vibrations

Under the forced oscillations understand those of them that occur under the influence of an external force that performs work that changes in time. There is another wording. Due to the external influx of energy, it is maintained in the system itself at a sufficient level so that the actual oscillations occur. To understand this, it is necessary to draw parallels with reality.An example of an object that performs such a type of oscillation is a swing, on which one person sits, and the second one swings it. There is one nuance. If an external force compensates for the loss of energy in the system continuously or periodically, without stopping the process of oscillation itself, they are called non-fading forced.

On the range can be noted the following. The amplitude of forced oscillations is completely determined by the force that acts from the outside, as well as by the ratio between the natural frequencies of the parties involved in the process. And here there is one interesting phenomenon. With forced oscillations, periodically you can observe a sharp increase in amplitude, which is called resonance.


mechanical vibrations

It occurs in cases where the force that affects the system becomes very close to its oscillation frequency. Another option is possible. In the event that the frequency of the influencing force is a multiple of the oscillations of the system itself, on which it acts, resonance also occurs. How is it graphically depicted? The dependence of the amplitudes of the system oscillations on the frequency of the affecting force is expressed using the resonance curve.

mechanical oscillations formula

Auto oscillations

Their use of self-oscillation found in the technique. They exist where sustained oscillations are maintained thanks to the energy source, which can automatically turn on and off the system itself. In such cases, you can seriously consider the issue of assigning a self-oscillatory status to the system. Why? The moment when you need to supply energy for oscillation, tracks the subsystem responsible for the feedback. Depending on the parameters of the body, it can influence strongly and immediately, or gradually and gradually. It can open or close the opportunity for energy to flow into the overall system. This is her main task. As an example of a self-oscillating system, we can recall a pendulum clock, where the energy source is a weight, and the anchor mechanism successfully copes with the role of a feedback subsystem that controls the flow of kinetics, on which mechanical vibrations depend.

Parametric oscillations

Under this type of oscillation are defined those that occur in systems that periodically change their parameters. What can you say about them? The only thing that determines the amplitude and strength of the oscillating system is its parameters.

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