# Young’s Modulus Spring Resonant Frequency Calculator

Calculate the frequency at which a spring oscillates by considering factors such as Young’s modulus, density, and other given values.

The resonance frequency of a spring can be determined using the formula 1/2(√(k/m)). In cases where the mass (m) is unknown, the resonance frequency can be calculated by substituting the mass with the product of density and volume (m = density x volume). This equation incorporates factors such as Young’s modulus, material density, and other provided values to determine the spring resonance frequency.

Wire Diameter
mm
Spring Diameter
mm
Total Number of Coils
Spring Material Shear Modulus
Material Density
ρ
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f_{\text{res}} = \frac{d}{{9 \cdot D^2 \cdot n_f}} \cdot \sqrt{\frac{G}{\rho}}

Where:

• fres = Spring Resonant Frequency
• d = Wire Diameter
• D = spring Diameter
• nf = Total Number of Coils
• G = Youngs Modulus of Material
• ρ = Material Density