Gavin, Henri P. 2018. Dynamics of Simple Oscillators (single degree of freedom systems). Department of Civil and Environmental Engineering
Duke University. Notes. 39 pp.
This document describes free and forced dynamic responses of simple oscillators (sometimes called single degree of freedom (SDOF) systems). The prototype single degree of freedom system is a spring-mass-damper system in which the spring has no damping or mass, the mass has no stiffness or damping, the damper has no stiffness or mass. Furthermore, the mass is allowed to move in only one direction. The horizontal vibrations of a single-story building can be conveniently modeled as a single degree of freedom system.
Part 1 of this document describes some useful trigonometric identities.
Part 2 shows how damped oscillators vibrate freely after being released from an initial displacement and velocity.
Part 3 covers the response of damped oscillators to persistent sinusoidal forcing.
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