Free and Forced Vibration

Free Vibration

When you study about Mechanical Vibration, the terms ‘free vibration’ and ‘forced vibration’ are usually the basic terminologies introduced in the beginning. The ‘forced vibration’ maybe easier to understand, but the ‘free vibration’ could be somewhat confusing, especially of where the term free comes from.

The animation below shows an example of a traditional baby cradle utilising a helical spring. Disturbance is given to initiate the system into motion and afterwards, the system is free to vibrate by itself. Here, the frequency of the motion (how fast it vibrates?) is proportional to the ratio of the stiffness constant (of the spring) and the mass (of the baby). We call this the “natural” frequency.

Free vibration is defined as the vibration case when no external force is working on a system while the system is in motion. The motion is the result of interchange of inertial force (kinetic energy from the baby mass) and the potential energy (from the helical spring).

Of course in reality, the motion will eventually stop because of the presence of damping property in the spring. The friction of atoms or plane cross section in the spring material converts the kinetic energy into heat energy. Without this damping mechanism, the baby cradle will bounce forever.

Without this damping mechanism, the baby cradle will bounce forever.

Forced Vibration

On the other hand, forced vibration is when there is an external force that drives the motion of the system. Thus the frequency of the motion follows the frequency of the external force.

Most of vibration cases we see in practice are considered as forced vibration, for instance the vibration of car or aircraft structures due to force from the reciprocating engines, vibration of a building roof due to force from the operating service equipments, bridge vibration when motor vehicles are passing by, and piping vibration due to the induced fluid flow inside the pipe.

Animated illustration of free and forced vibration.

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