Many objects in nature can be thought of as "mass-spring-systems" because they are composed of objects which have inertial mass as well as a spring like stiffness. It is natural for mass spring systems to enter into sinusoidal oscillation. These oscillations may create vibrations of the surrounding air (i.e. periodic sounds), as described under "sound propagation" below.
This figure is an animated version of Figure 1-1 of "Auditory Neuroscience"