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Wind Engineering: A Handbook for Structural Engineers by Henry Liu - University of Missouri—Columbia

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Appendix Basic Concepts on One-Dimensional Vibration

A prerequisite for understanding the complex behavior of structural vibration is the basic concept of one-dimensional (single-degree-of-freedom) vibration of a mechanical system. Several cases of such vibration are described next.

Undamped Free Vibration

Suppose a mass m is attached to a spring having a stiffness constant k. Without damping and without forcing function, we have the following,

image

where X is the displacement of the mass from its equilibrium position and image represents the second derivative ...

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