Hello,

Simple harmonic motion is important in research to model oscillations for example in wind turbines and vibrations in car suspensions. There is a close connection between simple harmonic motion and periodic waves; in most periodic waves, the particles in the medium experience simple harmonic motion. In a longitudinal wave, such as a sound wave, the particles oscillate along the direction of motion of the wave.

Simple harmonic motion is not a waves because waves  are phenomena not objects. The oscillating object does not lose any energy in SHM.  In harmonic motion there is always a restorative force, which acts in the opposite direction of the velocity. The restorative force changes during oscillation and depends on the position of the object.

Hope this helps!!!