Natural Frequency (mass-spring)⚠ unverified
Physics / Vibration · Undamped natural frequency of a mass-spring system
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| mass | m | kg | 1.0 | Mass |
| stiffness | k | N/m | 100.0 | Spring stiffness |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| wn | ωn | rad/s | Natural frequency |
The science & history
Understanding the Parameters
- $m$ — larger mass → lower $\omega_n$.
- $k$ — stiffer spring → higher $\omega_n$.
- $\omega_n$ — free oscillation rate with no damping; still the reference frequency when light damping is present.
Derivation (Approaching a Proof)
Newton: $m\ddot{x} = -kx$ ⇒ $\ddot{x} + (k/m)x = 0$. Characteristic frequency $\omega_n^{2} = k/m$.
History
The harmonic oscillator is the prototype of vibration theory and of second-order control plants.
Related Concepts: Damping Ratio, Damped Natural Frequency, Resonance Frequency damped, Magnification Factor
Notes: Registry calculator natural-frequency-mass-spring (unverified). Ideal undamped SDOF.