Existence of periodic solutions is obtained by using the max-min methods on the non-autonomous second order systems under the conditions of liner-growth.

This paper studies the existence of periodic solutions for some non-autonomous second order systems.

In this paper,we considered the existence and uniqueness of almost periodic solution to a class of second order nonautonomous system,also gave that only if a 1>0,a 2k+1 ≥0, x¨ +R(∑nk=0a 2k+1 x 2k+1 )′ x· +1L∑nk=0a 2k+1 x 2k+1 =Ae(t),(e(t) is an almost periodic function in some conditions) exists almost periodic oscillations,the results in [1-3] are extended and improved.

Step response to the second-order system with zero;

Analysis and application of performance index for transient responseof second-order system;

This system includes oscilla-tor, second-order system, counter, decoder,circuit and Helmholtz coils etc.

Existence of periodic solutions of a class of second order systems at resonance;

Standard second order system index mark form and the interaction between time-frequency performance and system characteristic parameter are discussed;the correlation of system time-frequency performance index is founded;all of these show the practical significance in different analytical domains reflecting system dynamic performance.