Wrong values for eigenvalues and frequencies

In summary, the problem involves solving for eigenvalues and natural frequencies. The provided MATLAB code and work in a PDF file are used to compute the frequencies, but they do not match the exact solution. The discrepancy may be caused by using the wrong formula for natural frequencies, inconsistent units, or errors in the code. It is recommended to check these factors for a correct solution.
  • #1
roldy
237
2

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
 

Attachments

  • determinant.pdf
    61.7 KB · Views: 282
  • determinant.txt
    343 bytes · Views: 389
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  • #2


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!
 

FAQ: Wrong values for eigenvalues and frequencies

What are eigenvalues and frequencies?

Eigenvalues are a set of numbers that represent the amount of stretch or compression a linear transformation produces in a particular direction. Frequencies, on the other hand, refer to the number of occurrences of a repeating event per unit of time. In the context of physics and engineering, eigenvalues and frequencies are often used to describe the behavior of a system.

Why do wrong values for eigenvalues and frequencies occur?

Wrong values for eigenvalues and frequencies can occur due to several reasons. One possible cause could be errors in the data used to calculate these values. Another reason could be incorrect assumptions or simplifications made in the mathematical model used to determine them. Additionally, numerical methods used to compute these values can sometimes introduce errors.

How can we verify the accuracy of eigenvalues and frequencies?

The accuracy of eigenvalues and frequencies can be verified by comparing them with results obtained from other methods or experimental data. It is also important to check for consistency with physical laws and principles. Additionally, testing the sensitivity of these values to changes in the input data or model assumptions can help identify any potential errors.

Can wrong values for eigenvalues and frequencies affect the overall results of a study?

Yes, wrong values for eigenvalues and frequencies can significantly impact the results of a study. These values are often used to make predictions about the behavior of a system, and incorrect values can lead to inaccurate conclusions or faulty designs. It is crucial to ensure the accuracy of these values to avoid any potential errors in the study.

What can be done to prevent wrong values for eigenvalues and frequencies?

To prevent wrong values for eigenvalues and frequencies, it is important to carefully review and validate the data used to calculate them. It is also crucial to thoroughly check the assumptions and mathematical models used to determine these values. Additionally, using multiple methods for computing these values and comparing the results can help identify any potential errors. Regularly updating and refining these values based on new data or experimental results can also improve their accuracy.

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