Young’s Modulus Spring Resonant Frequency Calculator
This calculator estimates the resonant frequency of a spring using geometric parameters, material density, and modulus of rigidity (G). It is ideal for evaluating coil spring dynamics in precision mechanical, automotive, and vibration systems.
Spring Resonance Estimator Using Shear Modulus
Spring Resonant Frequency with Young’s or Shear Modulus
Where:
- $$f_{\text{res}}$$ = resonant frequency (Hz)
- $$d$$ = wire diameter (m)
- $$D$$ = coil diameter (m)
- $$n$$ = number of active coils
- $$\rho$$ = material density (kg/m³)
- $$G$$ = shear modulus (Pa)
This formula derives from spring-mass dynamics and material elasticity, assuming no damping.
Young’s Modulus Spring Resonant Frequency – Calculation Example
Given:
- $$d$$ = 0.003 m
- $$D$$ = 0.03 m
- $$n$$ = 8
- $$\rho $$= 7850 kg/m³ (steel)
- $$G$$ = 79.3 × 10⁹ Pa
Calculation:
- $$f_{\text{res}} = \frac{0.003}{0.03^2} \cdot \sqrt{ \frac{9 \cdot 79.3 \cdot 10^9}{8 \cdot 7850} }$$
- $$= \frac{0.003}{0.0009} \cdot \sqrt{ \frac{713.7 \cdot 10^9}{62800} }$$
- $$≈ 3.33 \cdot \sqrt{1136226.11} ≈ 3.33 \cdot 1065.2 ≈ 3547~\text{Hz}$$
The resonant frequency of a coil spring can be accurately modeled using the wire’s geometry, density, and elastic modulus. This calculator is essential for engineers designing suspension systems, vibration isolators, and mechanical resonators, where precise frequency control is required. It allows designers to explore how changing wire diameter, number of coils, or material affects dynamic performance.