Spring Resonant Frequency Calculator
This calculator determines the resonant frequency of a mass-spring system based on the mass and spring constant. It’s essential for analyzing mechanical vibrations, oscillations, and tuning dynamic systems in engineering and physics.
Natural Frequency of Spring-Mass System
Spring Resonant Frequency Formula
Where:
- $$f$$ = resonant frequency (Hz)
- $$k$$ = spring constant (N/m)
- $$m$$ = mass attached to the spring (kg)
This formula assumes no damping and linear elastic behavior.
Spring Resonant Frequency – Calculation Example
Given:
- $$k$$ = 200 N/m
- $$m$$ = 2 kg
Calculation:
- $$f = \frac{1}{2\pi} \cdot \sqrt{\frac{200}{2}} = \frac{1}{6.283} \cdot \sqrt{100} = \frac{1}{6.283} \cdot 10 ≈ 1.59~\text{Hz}$$
The resonant frequency of a spring-mass system determines how fast it naturally oscillates when disturbed. This is a fundamental concept in mechanical engineering, acoustics, and vibration analysis. Knowing the natural frequency helps avoid resonance in structures, optimize damping, or deliberately tune systems for harmonic response, like in sensor or actuator design.