Free Vibrations of a Spring-Mass-Damper System

The derivation here follows the usual form given in [1], in which , , and are the mass, damping coefficient, and spring stiffness, respectively. The variable in this system is . Applying Newton's second law gives the differential equation , where and .


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[1] S. Timoshenko, D. Young, and W. Weaver Jr., Vibration Problems in Engineering, 4th ed., New York: John Wiley & Sons, 1990.


Contributed by: Stephen Wilkerson (Army Research Laboratory and Towson University), Nathan Slegers (University of Alabama Huntsville), and Chris Arney (United States Military Academy, West Point)
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