How do you find angular frequencies in coupled masses using Hooke's Law?

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Homework Help Overview

The discussion revolves around finding the angular frequencies of a system of three coupled masses connected by springs, utilizing Hooke's Law. The original poster is attempting to derive the equations of motion for each mass under the assumption of simple harmonic motion.

Discussion Character

  • Exploratory, Problem interpretation

Approaches and Questions Raised

  • The original poster presents equations of motion for each mass but expresses uncertainty about their correctness. Participants inquire about the details of the system and suggest that sharing more information could help identify any mistakes.

Discussion Status

The discussion has progressed with the original poster sharing their equations, although they initially struggled with them. A request for clarification through a diagram was made, but the original poster later indicated they resolved their issue independently.

Contextual Notes

The original poster's equations include terms that suggest a misunderstanding of the system's configuration, which was not fully clarified until later in the discussion.

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Homework Statement


There are 3 masses connected by springs of the same spring constant (k). The end masses are connected to solid walls via 2 more springs. Assuming simple harmonic motion find the angular frequencies (\omega) for each of the normal modes of vibrations...

Homework Equations


The Attempt at a Solution


I just need help getting the equations of motion for each of the masses, I can't seem to get them right
 
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What have you got so far? Posting your work may assist everyone in spotting out your mistake :smile:
 
So far I have got:

Mass A:

ma_{A} + kx_{B} - kx_{C} = 0

Mass B:

ma_{B} + kx_{A} - 2kx_{B} + kx_{C} = 0

Mass C:

ma_{C} + kx_{A} - kx_{B} + 2kx_{C} = 0

Thats the best I can do... :S

Sorry, the superscripts are meant to be subscripts XD
 
Could you please describe or draw the system? I cannot deduce any system that matches your equations.
 
hey, sorry for not putting up a diagram. didn't think to do that XD

It's okay though, I worked it out finally.

Thanks for trying to help :)
 

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