First-Order Systems

Reza N. Jazar
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Reza N. Jazar: RMIT University, School of Engineering

Chapter Chapter 5 in Advanced Vibrations, 2022, pp 399-479 from Springer

Abstract: 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].

Date: 2022
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DOI: 10.1007/978-3-031-16356-2_5

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