newtonian mechanics - Derive equation for a cantilever in SHM

I am currently investigating how a hacksaw blade's time period of oscillation changes when I add mass to the end of it or when I change the length it is clamped at.

I found the following equation from an IB worksheet:

$$ T^2=\frac{16M\pi^2x^3}{bEd^3} $$

Where:

• $T$ is the time period for one oscillation;


• $M$ is the mass of the cantilever;


• $x$ is the length of the cantilever;


• $b$ is the breadth of the cantilever and $d$ is the thickness of the cantilever;


• and $E$ is the stiffness of the cantilever.

I've looked around the internet and asked my teachers, but I haven't been able to derive this equation from first principles or the equations given in my syllabus.

If anyone knows where this comes from or would like to try and work it out, I would be very greatful.