Mass of cantilever vibrating at natural frequency

[Link]

Homework Statement

Find mass of vibrating steel cantilever. It is fixed at one end and got a mass on the other (free) end. Find the mass required when it is vibrating at w(natural) = 1800 rev/min.

Lenght: 50mm
width: 7mm
Thickness: 1mm

Homework Equations

w = sqrt(k/m)

The Attempt at a Solution

w is known, need to find k to plug into equation to solve for m.

k is not given but from formula booklet the end deflection for a cantilever with force applied at free end is: wL*L /2EI

Can I assume the end deflection will act as the stiffness k?
In this case the width and the Lenght and youngs modulus E is known, but how do I find I?
If it is known, k can be found and hence m.

 

[anathema]

To find the mass of the vibrating steel cantilever, we need to use the equation w = sqrt(k/m), where w is the natural frequency of vibration, k is the stiffness of the cantilever, and m is the mass of the cantilever.

Since the cantilever is fixed at one end, we can use the formula for end deflection, wL*L/2EI, where w is the force applied at the free end, L is the length of the cantilever, E is the Young's modulus of the material, and I is the area moment of inertia.

To find I, we can use the formula I = (b*h^3)/12, where b is the width of the cantilever and h is the thickness. Plugging in the given values of b = 7mm and h = 1mm, we get I = 0.0000417 m^4.

Now, we can plug in all the known values into the end deflection formula to solve for k. Once we have k, we can use the equation w = sqrt(k/m) to solve for m.

Hope this helps. Happy calculating!