Single Degree of Freedom

Definition

The simplest vibratory system can be described by a single mass connected to a spring (and possibly a dashpot). The mass is allowed to travel only along the spring elongation direction. Such systems are called Single Degree-of-Freedom (SDOF) systems and are shown in the following figure,

Equation of Motion for SDOF Systems
SDOF vibration can be analyzed by Newton's second law of motion, F = m*a. The analysis can be easily visualized with the aid of a free body diagram, The resulting equation of motion is a second order, non-homogeneous, ordinary differential equation:  with the initial conditions,  The solution to the general SDOF equation of motion is shown in the damped SDOF discussion.