Measuring young's modulus from simple harmonic motion

[TheCapacitor]

Homework Statement

I was doing this experiment: http://practicalphysics.org/shm-cantilever.html

I'm interested in the derivation of the result ω^2 = Exy^3 / 4*M*L^3. I tried to think where it comes from.

How do we even start to derive k from the equation mg = KS where S is the delta in the length of C.M before and after Mass was put on the edge and K is constant which is equal to Eb^3*a/4L^3?

Homework Equations

ω^2 = Exy^3 / 4*M*L^3

mg = KS where S is the delta in the length of C.M before and after Mass was put on the edge and K is constant which is equal to Eb^3*a/4L^3

The Attempt at a Solution

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Let's say theta is small so sin(theta) is approximately theta. I tried to make moment of forces equation with point of turning at the place of force N, but it really don't make any sense as we get thetamgL/2 + MgLtheta = 0.

 

[Chestermiller]

This result seems to neglect the mass of the ruler compared to the mass of the object taped to the ruler. They want you to treat the beam the same way you treat a massless spring.

What they are using is the equation, derived from solid deformation mechanics, for the downward displacement at the location were a force is applied to a cantilever beam as a function of the magnitude of the force. They don't want you to worry about where the equation came from.