Formula for Free Resonating Frequency of Cantilever to the Deflection

[nyxynyx]

Is there a formula relating the free resonating frequency of a cantilever to its deflection? Thanks!

 

[Gokul43201]

The resonant frequency is a function of material and geometric properties of the beam and is independent of the deflection.

For a cantilever beam of uniform cross-section,

$$f=\frac{1}{2\pi} \sqrt {\frac{8EI}{\rho Al^4}}$$

I: moment of inertia (depends on cross section)
E: Young's modulus
$\rho$: density
A: cross-section area
$l$: length