# Resonance

It is the phenomenon that happens when a physical system receives energy through frequency excitations equal to one of its natural vibration frequencies. Thus the physical system begins to vibrate with increasing amplitudes.

Each vibrating physical system has one or more natural frequencies, that is, which are characteristic of the system, more precisely the way it is built. For example, a pendulum being pushed off balance, strings on a guitar, or a pedestrian bridge over a busy highway.

All these systems have their characteristic natural frequency. When periodic excitations occur over the system, such as when the wind blows constantly over a bridge during a storm, a wave overlapping phenomenon occurs that changes the energy of the system, changing its amplitude.

As we have studied earlier, if the natural oscillating frequency of the system and the constant excitations about it are at the same frequency, the energy of the system will be increased, causing it to vibrate with increasing amplitudes.

A very famous case of this phenomenon was the breach of the Tacoma Narrows Bridge in the United States on November 7, 1940. At one point the wind began to blow as often as the bridge's natural oscillation, causing it to begin to rise. the amplitude of its vibrations until its structure could no longer bear, causing its structure to break.

The case of the Tacoma Narrows Bridge can be considered a human failure, since the wind that blew on 7 November 1940 had a frequency characteristic of the region where the bridge was built, so the engineers responsible for its construction failed to analyze the characteristics. of the region. For this reason, an in-depth analysis of all possible features that may require a change in a building construction is currently made.

Imagine that this is a suspension bridge, and its natural oscillation frequency is given by:

When periodically excited by a frequency wind:

The amplitude of oscillation of the bridge will be given by the superposition of the two waves:

If the bridge does not have a resistance that supports the range of motion, it will be damaged and may even be destroyed like the Tacoma Narrows bridge.