# What is “normal” about normal frequencies and normal modes?

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• AntonPannekoek
In summary, the term "normal" in the context of normal frequencies and normal modes in coupled oscillations can have multiple meanings. It could refer to "normal coordinates" which are locally orthogonal, or it could mean "orthogonal" in a general sense. The original meaning of "normal" is perpendicular, but in modern usage it can also mean the usual state or condition. In terms of the "normal distribution," the term was originally coined with reference to the "normal equations" involved in its applications, but over time it has also come to mean typical or common.

#### AntonPannekoek

So, my question is what does the "normal" part mean when one talks about normal frequencies and normal modes in coupled oscillations. Does it have to do with the normal coordinates that one uses when solving some problems, or with normal in the sense of orthogonal. Thanks for your help.

I don't know the etymology of the term, but 'normal' as 'orthogonal' would certainly work, because the normal modes correspond to eigenvectors of a matrix, and those eigenvectors will be orthogonal to one another.
'Normal coordinates' in Differential Geometry are coordinates that give a locally orthogonal basis, so 'normal coordinates' could also be based on 'orthogonal'.

vanhees71
The original meaning is perpendicular. In classical Latin normalis was a carpenter's square, and the word was also used for rectangular shapes made according to the carpenter's square. In Late Latin (in the early middle ages) it could mean perpendicular, or regular, in conformity with rule. The modern meaning of 'usual state or condition' (without explicit rules) seems to have developed in the 19th century. (See dictionary)

vanhees71
In English works they were often referred to as "characteristic modes," which I think describes their role well. The German words eventually too over.

"Normal" in the "normal distribution" may need some clarification as well. Gauss himself coined the term with reference to the "normal equations" involved in its applications, with normal having its technical meaning of orthogonal rather than "usual". However, by the end of the 19th century some authors started stating that this distribution was typical, common – and thus "normal". (wikipedia)

## 1. What is the meaning of "normal" in normal frequencies and normal modes?

The term "normal" refers to the most common or typical frequencies and modes of vibration that are observed in a given system or object. These frequencies and modes are considered normal because they are the most frequently occurring and are therefore used as a reference point for comparison.

## 2. How are normal frequencies and normal modes determined?

Normal frequencies and modes are determined through mathematical calculations and experiments. The equations used to calculate these values take into account the physical properties of the system or object, such as mass, stiffness, and damping. Experiments can also be conducted using instruments such as a frequency analyzer or oscilloscope to directly measure the frequencies and modes of a system.

## 3. What is the significance of normal frequencies and normal modes in science?

Normal frequencies and modes are important in a variety of scientific fields, including physics, engineering, and acoustics. They provide valuable information about the behavior and properties of a system or object, and can be used to predict its response to different stimuli or conditions. In addition, normal modes are often used in the design and optimization of structures to ensure their stability and functionality.

## 4. Can normal frequencies and normal modes change over time?

Yes, normal frequencies and modes can change over time due to external factors such as temperature, humidity, and wear and tear. These changes can be small or significant, depending on the system or object in question. In some cases, changes in normal frequencies and modes can also be intentional, such as in musical instruments where tuning is adjusted to produce different notes or tones.

## 5. What is the relationship between normal frequencies and normal modes?

Normal frequencies and modes are closely related as they both describe the vibration and oscillation patterns of a system or object. Normal frequencies are the specific frequencies at which a system or object naturally vibrates, while normal modes are the corresponding patterns of motion that occur at these frequencies. In other words, normal modes are the different ways in which a system or object can vibrate at its normal frequencies.