O Naprzemienności Ruchu przy Pewnym Tłumieniu Nieliniowym

The author is concerned with the investigation of the motion described by the equation (1.1).
For damping characteristics satisfying the condition R(x)x > ) in a certainfinite or infinite interval (-V, V). He establishes certain of the oscillatory characteristics of the motion. Making use of Refs. [1], [2] supplementing them with his own considerations, he finds that the oscillatory nature of the motion depends only on the coefficient of the first power of the power expansion of the function R(%). The notion of the «critical line » is introduced. The oscillatory character of the motion is determined by the mutual position of the critical
line and the damping characteristic R(%). It is also shown that in the non-alternating case a motion is possible for which the deflection has at most one zero independent of the initial conditions, or a finite number of zeros depending on the initial conditions. Mathematical and graphical criteria are
given for the distinction between the two cases.