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Work in Progress: Connections Between First-Order and Second-Order Dynamic Systems – Lessons in Limit Behavior

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2018 ASEE Annual Conference & Exposition


Salt Lake City, Utah

Publication Date

June 23, 2018

Start Date

June 23, 2018

End Date

July 27, 2018

Conference Session

Dynamic Pedagogies for Engineering Dynamics

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Vincent C. Prantil Milwaukee School of Engineering

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Dr. Vincent Prantil earned his BS, MS, and PhD degrees in Mechanical And Aerospace Engineering at Cornell University. He has worked as a senior member of technical staff in the Applied Mechanics and Materials Modeling Directorates at Sandia National Laboratories in Livermore, California where he was a co-recipient of the R&D100 Award for development of Microstructure-Property Model Software in 2000. He has published 31 peer-reviewed journal and conference papers in the areas of finite element analysis, crystal plasticity, response of dry granular materials, fluid power hydraulics, heat treatment distortion, and teaching methods for undergraduate mechanics curricula. He has been a faculty member at the Milwaukee School of Engineering since 2000 in the Mechanical Engineering Department where he has taught 20 courses ranging from undergraduate mechanics, dynamics, modeling, simulation, finite element analysis and numerical methods to capstone design. In addition to teaching undergraduate engineering core curriculum courses, Dr. Prantil is currently co-authoring a book on Finite Element Simulation of Case Studies for Undergraduates.

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Mark L. Nagurka Marquette University

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MARK NAGURKA, Ph.D. is an Associate Professor of Mechanical and Biomedical Engineering at Marquette University. He received his B.S. and M.S. in Mechanical Engineering and Applied Mechanics from the U.of Pennsylvania and a Ph.D. in Mechanical Engineering from M.I.T. He taught at Carnegie Mellon before joining Marquette University. His professional interests are in the design of mechanical and electromechanical systems and in engineering education. He is a Fellow of the American Society of Mechanical Engineers (ASME).

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Work-in-Progress: Connections Between First-Order and Second-Order Dynamic Systems - Lessons in Limit Behavior

Mark L. Nagurka, Vincent C. Prantil


There exists a unique relationship between the natural frequency and damping ratio of a lumped-parameter second-order dynamic system and the time constants of equivalent first-order systems. These first-order systems result in the limit of vanishing stiffness or inertia, with the system then capable of storing only a single type of energy. To emphasize the correspondence of first-order-like behavior with storage of primarily one type of system energy, a pair of two degree-of-freedom systems, one inertia-dominated and one stiffness-dominated, are presented. Although the governing ordinary differential equations are second-order, these systems are overdamped only. In studying limiting behaviors, the paper raises the question of what it means for a system that can never be underdamped to possess a natural frequency. The paper shows that expressions for natural frequency and damping ratio can be explicitly written in terms of pairs of time constants that arise naturally from the limiting process. The analysis is presented in a way that is amenable to undergraduate engineering students in courses in system dynamics.

Prantil, V. C., & Nagurka, M. L. (2018, June), Work in Progress: Connections Between First-Order and Second-Order Dynamic Systems – Lessons in Limit Behavior Paper presented at 2018 ASEE Annual Conference & Exposition , Salt Lake City, Utah. 10.18260/1-2--31278

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