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Dynamics of structures with MATLAB® applications by Ashok K. Jain

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Chapter 2

Single Degree of Freedom System: Free Vibrations

2.1 Introduction

It is interesting to analyse a single-degree-of-freedom (SDOF) system as shown in Figure 2.1 when it vibrates freely under its own characteristics, that is, when external force p(t) is absent. Naturally its motion will not be influenced by the nature, frequency and duration of the external force. It is called a free vibration analysis. It is assumed that the spring and damper are massless. A damper is also referred to as a dash-pot system. A SDOF system moves over a smooth and frictionless surface represented by rollers in Figure 2.1. Damping plays a very significant role in the dynamic response of a structure by dissipating vibrational energy. Damping is an inherent ...

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