Many mechanical systems, such as car suspensions or a swing, have the ability to oscillate. In these systems, you often have a mass (or an inertial equivalent) that is attached to a spring-like component. When this mass-spring system is displaced from its equilibrium position and then released, it will oscillate, or swing back and forth.

A simple example of this is the suspension of a car. The car acts as the mass and a substantial spring supports the body of the vehicle on the subframe. When the car goes over a bump in the road, it causes the suspension to oscillate.

When there is little or no friction in a system, the oscillations can continue for a long time. These are known as free vibrations.

The frequency at which a mass-spring system oscillates when displaced from its equilibrium position and released is called the natural frequency (f₀). This frequency depends on the mass (m) and the spring constant (k) of the system. The formula for the natural frequency is - f₀ = 1 / (2π) √(k/m)