What does 'simple harmonic motion' mean?

[MIA6]

What does 'simple harmonic motion' mean? By definition, it describes any periodic motion that is the result of a restoring force that is proportional to displacement. What does 'periodic' mean here? It means recurring at equal intervals of time? Ususally, the example of SHM is virating mass-spring system. But the definition of SHM is sort of according to the formula, so I don't really get its essence. Is simple harmonic motion simply a back-and-forth motion over the same path? In the 'wave', it says that a wave whose source vibrates with simple harmonic motion is called a sine wave. Once again, what does SHM really mean?
Thanks.

 

[Mindscrape]

It's as the name describes: some sort of motion that has a defined harmonic (frequency), and one that can be described with a relatively simple equation.

-Periodic does mean recurring at equal intervals of time.
-I don't know if back and forth motion is the best descriptor, but yes it is about a motion that can be modeled by waves.
-The wave can be either sine or cosine.

The examples, of course, include a mass and a spring, a pendulum, and even atomic vibrations.

 

[andrevdh]

The position of the oscillator can be described mathematically by a sine (or cosine) varying function of time. What can be simpler than that?

 

[chaoseverlasting]

Its a simple back and forth motion. The equation (y=asinwt or y=acoswt) describes an oscillating point on the y or x respectively axis of a circle with radius 'a' centered at the origin.