This oscillation will be about a reference point or equilibrium position. A good example most of us are familiar with is a pendulum. Held vertically, the equilibrium position is where the pendulum is aligned vertically. Vibration is a result of dynamic forces in machines that have moving parts and in structures that are connected to the machine. Different parts of the machine will vibrate with various frequencies and amplitudes.
Vibration can be a cause of noise and can lead to wear and fatigue of parts.
To describe vibration amplitude, displacement is used with its first and second derivatives in time, respectively velocity and acceleration. These are shown schematically in the figure. We can quantify the force on the system in terms of these units as well. The force produced by a spring is the displacement multiplied by the stiffness of the spring, k. Finally, there has to be a reaction force due to inertia of the mass.