Table of Contents
What Is Natural Frequency?
Natural frequency is the frequency at which a system tends to oscillate in the absence of any external driving or damping force. Every physical system that can vibrate has one or more natural frequencies determined by its physical properties such as mass, stiffness, and geometry. When excited at its natural frequency, the system resonates with maximum amplitude.
Understanding natural frequency is critical in engineering to avoid resonance failures, design musical instruments, tune suspension systems, and analyze structural dynamics. The simplest model is the spring-mass system, where the natural frequency depends only on the spring constant k and the mass m.
Formula
Where f is frequency in Hz, ωn is angular natural frequency in rad/s, k is spring constant in N/m, and m is mass in kg.
Applications
| Application | Typical Range |
|---|---|
| Car suspension | 1-2 Hz |
| Building sway | 0.1-1 Hz |
| Guitar string | 80-1200 Hz |
| MEMS sensor | 1-100 kHz |
Frequently Asked Questions
What happens at resonance?
When a system is driven at its natural frequency, resonance occurs and the vibration amplitude increases dramatically. Without damping, the amplitude would theoretically become infinite. In practice, damping limits the peak but resonance can still cause structural failure, such as the famous Tacoma Narrows Bridge collapse.
How does damping affect natural frequency?
Light damping slightly lowers the natural frequency. The damped natural frequency is ωd = ωn√(1-ζ²) where ζ is the damping ratio. For most engineering systems with low damping, the difference is negligible.