I Meaning of the word "Harmonic" in different contexts

[JTC]

A harmonic function is one that satisfies Laplace's equation -- a definition cannot be more precise than that.

However, in the study of vibrations, sine and cosine are considered harmonic functions; but they don't solve Laplace's equation.

And then there are words like: harmonics (for higher frequencies) or "harmonic oscillators" that repeat their motion.

Could someone provide a suite of definitions of the word harmonic?

At the moment, I am confused and thinking that the functions that solve Laplace are related to harmonic oscillators. Am I dealing with multiple definitions?

 

[jtbell]

Am I dealing with multiple definitions?

Probably. It's an unfortunate and confusing fact of life that many words have different meanings or definitions in different contexts.

 

[ericjericj]

I'd guess that harmonic in each case may have a common etymology from stringed instruments.

The wikipedia article here makes the connection between the harmonic series in music, harmonic mean, harmonic oscillators, etc. I don't know about the Laplace's equation piece of it though.

 

[WWGD]

Probably. It's an unfortunate and confusing fact of life that many words have different meanings or definitions in different contexts.

Talk aboutthe use of the term " Normal" in Mathematics: https://en.wikipedia.org/wiki/Normal#Mathematics

Talk about overloading notation.