Wrong values for eigenvalues and frequencies

[roldy]

Homework Statement

I'm working on a problem that involves solving for the eigenvalues and the natural frequencies. I've attached my work as a pdf file and also the MATLAB code used to get the result. The problem that I'm running into is that the frequencies computed from the determinant are not even close to the frequencies for the exact solution. For the frequencies, I'm only comparing the [itex]\sqrt{820\lambda}[/itex] and the (n[itex]\pi[/itex])² term. I have no idea where I am going wrong.

Homework Equations

shown on pdf document

The Attempt at a Solution

shown on pdf and MATLAB file included

 

[mighty2000]

Hello,

Thank you for sharing your work and code. I took a look at your problem and it seems like you are on the right track. However, there are a few things that might be causing the discrepancy between your computed frequencies and the exact solution.

Firstly, it seems like you are using the wrong formula for the natural frequencies. The correct formula is given by \sqrt{\frac{k}{m}}, where k is the stiffness and m is the mass. In your code, you are using the formula \sqrt{820\lambda}, which might be why your frequencies are not matching the exact solution.

Secondly, make sure that you are using the correct units for your values. The stiffness and mass values should be in consistent units, such as N/m and kg, respectively. If your units are not consistent, then your computed frequencies will also be incorrect.

Lastly, check your code for any errors or typos. It's always a good idea to double-check your code and make sure that all the calculations and formulas are correct.

I hope this helps. Good luck with your problem!