An Introduction to Mechanical Vibration

Single Degree of Freedom System

A single degree of freedom system consists of a mass, a spring, and a damper if the system is modeled as a damped system. The spring is modeled as a linear spring, which provides a restoring force. The damper is modeled as a viscous damper, which provides a damping force proportional to a relative displacement and acting in the direction against a velocity vector. If there is a driving force acting on the mass, the system vibrates under the driving force, which is called forced vibration. Otherwise, the system may vibrate under initial displacement and/or initial velocity, which is called free vibration.

Undamped Free Response

Damped Free Response

Forced Response