Mass-spring diagrams
Vibrations of industrial structures - Modeling, predictive and interpretation tools

In all cases, vibrations involve a permanent exchange between kinetic energy (associated with the vibratory speed and mass of the moving elements) and deformation energy (associated with the dynamic stresses linked to the rigidity of the elements deformed by the vibratory motion).

The most elementary way of representing these exchanges is to consider the oscillation of a rigid mass M (pure kinetic energy) supported by a massless spring of stiffness K (pure deformation energy). Simply write down the equilibrium of the system to find the well-known elementary equation, noting $\ddot{x}$ the second derivative of the...