# Time Response of First- and Second-order Dynamical Systems

• Jorge Angeles
Chapter
Part of the Mechanical Engineering Series book series (MES)

## Abstract

How physical systems, e.g., aircraft, respond to a given input, such as a gust wind, under given initial conditions, like cruising altitude and cruising speed, is known as thetime response of the system. Here, we have two major items that come into the picture when determining the time response, namely, the mathematical model of the system and the history of the input. The mathematical model, as studied in Chap. 1, is given as an ODE in the generalized coordinate of the system. Moreover, this equation is usually nonlinear, and hence, rather cumbersome to handle with the purpose of predicting how the system will respond under given initial conditions and a given input. However, if we first find the equilibrium states of the system, e.g., the altitude, the aircraft angle of attack, and cruising speed in our example above, and then linearize the model about this equilibrium state, then we can readily obtain the information sought, as described here.

## Keywords

Impulse Response Magnification Factor Bode Plot Unit Impulse Harmonic Response
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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