As the amplitude increases, the nonlinearity of the system gradually decreases. When the amplitude is large enough (A≥10h), the vibration of the system can be approximated as a simple harmonic vibration. According to the analysis, it can be concluded that the spring mass system has the following characteristics: 1) The nonlinear effect of the system is very significant when the vibration is small, and with the increase of the amplitude, the nonlinear effect is weakened, and the vibration of the system can be increased after the amplitude is increased to a certain value. Think of a simple harmonic motion. This is in contrast to common systems such as single pendulums, complex pendulums, soft springs, and hard spring oscillators. These systems have larger amplitudes and more pronounced nonlinear effects, while small vibrations can be considered linear vibrations. This result suggests that in the actual vibration study, all micro-vibration systems cannot be simply regarded as linear systems, and must be specifically analyzed.
The nonlinear effect of the spring mass system is very affected by the parameter h. When the system vibrates slightly, the difference in h can change the strength of the cubic nonlinearity of the Duffing oscillator. When h=l0, the system can be regarded as a cubic oscillator; when h is large, the system can be regarded as a linear system. This result will provide a mechanical experimental method that allows us to conduct a comprehensive experimental study of the properties of Duffing oscillators and cubic oscillators, which will be our next research work. In summary, this paper analyzes the motion of a class of simple spring mass systems, numerically solves and analyzes the obtained differential equations, and obtains the characteristics of the system's motion. The conclusions deal with the vibration problems in engineering design and other fields. Have a certain guiding significance.
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