Compute the oscillation frequency of a spring by taking into account variables like Young’s modulus, density, and other provided parameters.
The resonant frequency of a spring can be computed using the formula 1/2(√(k/m)). When the mass (m) is not given, the resonant frequency can be evaluated by replacing the group with the product of density and volume (m = density x volume). This equation integrates factors, including Young’s modulus, material density, and other provided values, to ascertain the resonant frequency of the spring.
Young\’s Modulus Spring Resonant Frequency formula
![\[f_{\text{res}} = \frac{d}{{9 \cdot D^2 \cdot n_f}} \cdot \sqrt{\frac{G}{\rho}}\]](https://x-calculator.com/wp-content/ql-cache/quicklatex.com-8a39b3e462fe3fadf0ed0646da82b3b8_l3.png "Rendered by QuickLaTeX.com")
Where:
- fres = Spring Resonant Frequency
- d = Wire Diameter
- D = spring Diameter
- nf = Total Number of Coils
- G = Youngs Modulus of Material
- ρ = Material Density
