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First-Order Systems

In: Advanced Vibrations

Author

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  • Reza N. Jazar

    (RMIT University, School of Engineering
    Xiamen University of Technology, School of Civil Engineering and Architecture)

Abstract

There are cases where the behavior of a dynamic system can be modeled by first-order or reducible to first-order differential equations. The motion of a first-order system with no external force is the natural motion. The solution of natural motion is an exponential function of time. The most important characteristic of first-order systems is their time constant. The response of a system after a period of one time constant reaches exp(1) of its initial value. A time constant is passed when x drops by about %64 of its initial value. The general natural motion of first-order systems is either exponentially decreasing or increasing function of time, and they do not show vibrations. The excited case of every linear first-order system is expressed by a full first-order equation. Any linear free vibrating system of any order can be expressed by a set of coupled first-order linear differential equations. The solution of the set of coupled first-order linear homogeneous equations is exponential with the coefficient matrix as the exponent [A].

Suggested Citation

  • Reza N. Jazar, 2022. "First-Order Systems," Springer Books, in: Advanced Vibrations, edition 2, chapter 0, pages 399-479, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-16356-2_5
    DOI: 10.1007/978-3-031-16356-2_5
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