Link between harmonic functions and harmonic oscillators?

[Navierstoked]

I'm a bit confused wether or not there is a link between harmonic functions (solutions of the Laplace pde) and harmonic oscillating systems? What is the meaning of "harmonic" in these cases? Thanks!

 

[mathman]

Harmonic in both physics and math usually refer to things which are periodic. In math it is usually used in descriptions involving sines and cosines. In physics it is usually used in discussing pendulums and such things.

 

[Navierstoked]

Harmonic in both physics and math usually refer to things which are periodic. In math it is usually used in descriptions involving sines and cosines. In physics it is usually used in discussing pendulums and such things.

Ok.. So are all the solutions of the Laplace equation (in complex analysis) periodic? By definition, they are harmonic. So is a harmonic function and a periodic function the same thing?

 

[mathman]

Harmonic functions are more general. I suggest looking things up on Wikipedia will give you a lot more details. The main point I was trying to make is that you need to separate mathematics and physics to clarify the understanding.