Free Vibration of Undamped Single-Degree of- Freedom Systems

Contents
1. Free Vibration of Single-Degree of- Freedom Systems
2. Free Vibration of an Undamped Translational System
3. Free Vibration of an Undamped Torsional System
1. Free Vibration of Single-Degree of- Freedom Systems
Free Vibration occurs when the system oscillates on its own due to initial
disturbance without any external forces. For instant a simple pendulum
oscillation and the motion of a swing after an initial disturbance.
A system shown in Figure.1 is a single-degree-of-freedom system, since one
coordinate (x) is sufficient to specify the position of the mass at any time.
2. Free Vibration of an Undamped Translational System
As the motion for the system in Figure.1 is linear therefore we can use
Newton s second law to derive the equation of motion as follow;
For transverse vibration
Deflection in transverse direction can be calculated as follow;
Free Vibration of an Undamped Torsional System
Torsional vibration occurs when a rigid body oscillates about a specific reference axis. Displacement of the body is measured in terms of an angular coordinate.