Forced oscillations in linear system with one degree of freedom at power affecting. The linear high-frequency injection unit. A resonance

The lecture purpose is deepening of concept "forced oscillations" at power and parametric affecting, revealing of features of a resonance of displacement, speeds and accelerations.

Forced oscillations result from external affecting on oscillatory system.

Discriminate two aspects of external affecting: power and parametric.

At power affecting on system superposed force F (t) acts. Taking in the capacity of an instance an electric oscillating circuit in which it is consecutive with L, C, R elements inject the oscillator of alternating voltage F (t) in a general view the equation of oscillations will look like:

. (1)

This equation generally the nonlinear. The circuit design of the oscillating circuit which is under power external affecting, is resulted on fig. 1. The variable х in this case represents an electric charge on the capacitor.

R

L

F (t)

Fig. 1. The Oscillating circuit at power affecting.

Parametric external affecting on system carry out change in a time of magnitude of one of parametres of oscillatory system. If in the capacity of an instance again to take an electric oscillating circuit in which variable parametre in a time is the capacity of the capacitor With the equation presenting oscillations in a contour, represented on fig. 2, will look like:

. (2)

R

L C (t)

Fig. 2. The Oscillating circuit at parametric affecting.

Lecture 6

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