I was able to derive a similar equation, but not the exact one you mention.
The differential equation of a beam can be stated as
where: E is the elastic modulus, I is the section area moment, ρ is the mass density, A is the section area and u(z,t) is the deformation as a function of position z and time t.
In your case,
manpreet Best Answer 2 years ago
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:
Where:
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.