**Classification of Vibration** – In general, vibrations can be classified into several ways:

**Free and Forced Vibration**

**Free Vibration**. If a system is initialised with interference, so it vibrates by itself, then the vibration is called free vibration. No external force works on the system. The motion of back and forth of a pendulum is an example of free vibration.

**Forced Vibration**. If a system is subjected to an external force (more precisely the repetitive force), then the vibrations that arise on the system is known as forced vibrations. The vibrations that arise on a working diesel engine is one example of forced vibration.

If the frequency of an external force is exactly same as the vibration frequency of the system, a condition known as resonance occurs. Resonance is very dangerous. Damage from the structures of buildings, bridges, turbines, and airplane wings is often associated with the resonance of the vibrations.**Undamped and Dumped Vibration**

If there is no energy lost or dissipated due to friction or other resistance during vibration, then the vibration is known as Undamped Vibration. Whereas, if a vibration experiences a gradual reduction of energy, it is called Damped Vibration. In various systems, the value of the damping is so small that it is often disregarded for most engineering purposes. But also vice versa, there are other systems that put damping system into important components, shock absorber in vehicles for example. Consideration of damping becomes extremely important in analyzing vibratory systems near resonance.**Linear and Nonlinear Vibration**

If all the basic components of a vibration system the spring, mass, and damper behave linearly, the resulting vibration is known as Linear Vibration. However, if one or more of these basic components behaves nonlinearly, then the vibration is called Nonlinear Vibration. Differential equations are made to describe the behavior of linear and nonlinear vibration systems. If the vibrations are linear, the superposition principle applies, and the mathematical analysis technique is well developed. For nonlinear vibrations, the superposition principle becomes invalid, and the analytics technique becomes more difficult. Since all vibration systems tend to behave nonlinearly as oscillation amplitude increases, knowledge of nonlinear vibrations is more developed in handling practical vibration systems.**Deterministic and Random Vibration**

If the value or magnitude of the excitation (force or movement) acting on the vibration system is known at any given time, the excitation is called deterministic, and the resulting vibration is known as Deterministic Vibration.

In some cases, excitation is nondeterministic or random; excitation values at certain times can not be predicted. In this case, extensive excitation data may indicate some statistical regularity. Under these conditions it is possible to estimate averages such as the mean and mean square values of excitation. Examples of random excitation are wind speed, roughness of the road, and ground movement during an earthquake. If the excitation is random, the resulting vibration is called Random Vibration. In this case the vibration response of the system is also random; and that condition can only be explained through statistical calculations.