What Is the Natural Angular Frequency of a Cantilevered Body?

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Homework Help Overview

The problem involves determining the natural angular frequency of a cantilevered body subjected to a load. The context includes a cantilever beam with a specified load and deflection, and participants are exploring the appropriate formulas and methods to calculate the frequency.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the application of Hooke's law and the differences in behavior between a spring and a cantilever beam. Questions are raised about the variables involved in the relevant formulas, specifically W, E, and I.

Discussion Status

There is an ongoing exploration of different approaches to the problem, with some participants suggesting alternative formulas for calculating the natural frequency. The discussion includes attempts to reconcile different methods and interpretations of the problem setup.

Contextual Notes

Participants note the need for clarity on the definitions of certain variables and the implications of using different formulas for cantilever beams compared to springs. There is also a mention of specific choices for the natural angular frequency that are provided in the original problem statement.

zorro
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Homework Statement



A body A weighing 22N is positioned on the end of a slender horizontal cantilever fixed at one end (mass of the plank is negligible). A force (vertically downwards) on A causes a deflection of 12.5mm. The natural angular frequency in rad/s of the body A is (nearly) ?

1)2
2)6
3)24
4)1.2

The Attempt at a Solution

F=kx
k=22/0.0125

w=(k/m)1/2=28rad/s, not in the choices. Did I make any mistake?
 
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Usually your method would work for a spring, but I think a cantilever is a bit different.

If you look in this thread, you will find a different formula

https://www.physicsforums.com/showthread.php?t=275927

You can get the value for EI/L3 using

deflection = PL3/3EI where P = load and L = length of beam
 
What are W,E and I?
 
Abdul Quadeer said:
What are W,E and I?

Actually now that I see that formula, it is essentially the same as what you did.

The most I can say is 24 rad/s would be the best answer given that you need to choose from those 4.
 

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