Question

What are damped vibrations? How do they differ from free vibrations? Give one example of each.

Answer 1

Vibration is a type of movement where an object moves back and forth. There are two types of vibrations; free vibrations and forced vibrations. Damped vibrations are a subset of forced vibrations where the force is applied to resist the motion of the system, while in free vibrations, there is no external force applied.

Complete answer:
Free vibrations are the type of vibrations where there is no external force provided to start or stop the vibrations of the particle. In an ideal condition, a free vibration would go on for an infinite time. Generally, the solution of a free vibration is a sinusoidal wave function. The amplitude of a free vibration remains constant throughout; hence it does not grow or decay.

In damped vibrations, there is an external force which affects the free vibration, it dampens or reduces the amplitude of the system. When an external force is provided to show resistance to the motion of the system, hence ultimately stopping the motion of the system, then such vibrations are called damped vibrations. Energy of the system is dissipated due to this external force such as friction or resistance.

The difference between free vibration and damped vibration is that in free vibration there is no external force, while in damped vibration, there is an external force. Also free vibrations can go on for infinite time, while damped vibrations cannot go on and have to stop.Examples of damped vibrations are carpet pads and shock absorbers in vehicles.

Note: Example of a free vibration is not possible, at least on earth. This is because regardless of how much initial force was applied to start the vibration or oscillation; there will be resistance to stop the motion of the system due to friction, viscosity or air resistance. So all the vibrations that one can observe are forced vibrations.