Damping and resonance

In a nutshell

When a system is forced to oscillate at its natural frequency, the system will resonate and its oscillations will quickly gain amplitude. Damping affects systems in different ways depending on how much damping is being applied. Systems can be lightly damped, heavily damped, critically damped or overdamped.

Free and forced vibrations

Free vibrations

If an object such as a mass on a spring is pulled from its equilibrium position and released it will undergo simple harmonic motion. The mass will oscillate at the systems natural frequency,

If there were no resistive forces acting on the system then the mass would continue to oscillate forever. This is what is called a free vibration.

Note: In reality moving things will transfer some energy into frictional forces such as air resistance, but the mass on the spring can still be considered to be a free vibration.

Forced vibrations

Take the same mass on a spring and attach it to a vibration generator. The mass on a spring is now being driven at the frequency of the vibration generator. This is called the driving frequency.

This is known as a forced vibration as the oscillation has being provided by an external driving force.

Resonance

When the driving force of an external oscillator is matched to the systems natural frequency, the amplitude of the system increases rapidly.

Note: Natural frequency is the frequency in which an object oscillates without an external driving force.

When this happens the system is said to be resonating.

The graph for amplitude against driving frequency for a system looks like this: