L36 : Free Vibration

The study of vibration is concerned with the oscillatory motion of bodies and the forces associated with them. There are two general classes of vibration- free and forced. Free vibration takes place when a system oscillates under the action of forces inherent in the system itself, and when external impressed forces are absent. The system under free vibration will vibrate at one or more of its natural frequencies, which are properties of the dynamical system established by its mass and stiffness distribution.

Vibrations that take place under the excitation of external forces is called forced vibration. When the excitation is oscillatory, the system is forced to vibrate at the excitation frequency. If the frequency of excitation coincides with one of the natural frequencies of the system, a condition of resonance is encountered, and dangerously large oscillations may result.

Simple Harmonic Motion :

A body is said to have simple harmonic motion if it moves in a straight line such that its acceleration is always proportional to its direction from a fixed point and is directed towards the fixed point.

Oscillatory motion may repeat itself regularly, such as spring mass or display considerable irregularity, as in earthquakes. When the motion is repeated in equal intervals of time T, it is called periodic motion. The repetition time T is called the period of the oscillation and its reciprocal

is called the frequency. If the motion is designated by the function x(t), then a periodic motion must satisfy the relationship