Free Vibration

  • Ahmed A. Shabana
Part of the Mechanical Engineering Series book series (MES)


The term free vibration is used to indicate that there is no external force causing the motion, and that the motion is primarily the result of initial conditions, such as an initial displacement of the mass element of the system from an equilibrium position and/or an initial velocity. The free vibration is said to be undamped free vibration if there is no loss of energy throughout the motion of the system. This is the case of the simplest vibratory system, which consists of an inertia element and an elastic member which produces a restoring force which tends to restore the inertia element to its equilibrium position. Dissipation of energy may be caused by friction or if the system contains elements such as dampers which remove energy from the system.

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • Ahmed A. Shabana
    • 1
  1. 1.Richard and Loan Hill, Professor of Engineering, Department of Mechanical & Industrial EngineeringUniversity of Illinois at ChicagoChicagoUSA

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