Introduction to the Linear Graph Method, Step Responses, and Superposition

  • Karl A. SeelerEmail author


System dynamics predicts the responses of physical systems to inputs of energy. In this chapter, we examine the response of first-order systems to step changes of the input power variable. The response of a system to a step input, called the system’s “step response,” is both common and important. It is common because many sources provide a reasonably constant value of the input variable, if power draw is not too large. The importance of the step response is twofold. First, the step response reveals the homogeneous response of the system. We can experimentally determine the elemental parameters of the system’s step response. Second, the superposition (or summing) of steps inputs of different amplitudes and shifted in time allows us to approximate any arbitrary input. Superposition is then used to calculate the response of a system to that input by summing the individual responses to each step.


Step Response Power Variable Heaviside Step Function Differential System Equation Linear Graph 
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References and Suggested Reading

  1. Hildebrand FB (1976) Advanced calculus for applications, 2nd edn. Prentice-Hall, Englewood CliffsGoogle Scholar
  2. Rowell D, Wormley DN (1997) System dynamics: An introduction. Prentice- Hall, Upper Saddle RiverGoogle Scholar
  3. Shearer JL, Murphy AT, Richardson HH (1971) Introduction to system dynamics. Addison-Wesley, ReadingGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Mechanical Engineering DepartmentLafayette CollegeEastonUSA

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