The natural frequency of oscillation refers to the frequency at which a system oscillates when no external forces are acting upon it.

When a system is displaced from its equilibrium position and allowed to oscillate freely, it does so at a specific frequency known as its natural frequency. This frequency is influenced by the physical characteristics of the system, including its mass, stiffness, and damping properties. The natural frequency can be computed using the following formula:

In this equation, $\omega$ represents the natural frequency in radians per second, $k$ is the spring constant measured in newtons per meter (N/m), and $m$ is the mass measured in kilograms (kg).

For instance, consider a mass-spring system with a mass of $0.5 \, \text{kg}$ and a spring constant of $10 \, \text{N/m}$. The natural frequency of this system can be determined as follows:

This result indicates that the system will oscillate at a frequency of approximately $4.47$ cycles per second (or hertz) when it is disturbed from its equilibrium position and allowed to oscillate freely.

The concept of natural frequency is crucial in various fields of physics and engineering, as it significantly affects the behavior of structures such as bridges, buildings, and electronic circuits. A thorough understanding of a system’s natural frequency enables engineers to design stable and efficient structures and devices.