Are these free-body diagrams correct (mass-spring-damper system)?

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The discussion revolves around verifying the correctness of free-body diagrams related to a mass-spring-damper system and the formulation of corresponding second-order ordinary differential equations. The original poster seeks feedback on their attempt, specifically questioning the accuracy of their diagrams and equations. Respondents encourage clarity on which parts of the solution are uncertain and suggest that some elements, like the x3 component, may not be necessary. Overall, the focus is on ensuring the equations accurately represent the physical system in question. The conversation emphasizes the importance of understanding and validating each part of the analysis.
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Problem: Write the equations as a set of two, second-order ordinary differential equations.

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My attempt…does it look correct? Thanks in advance!

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Where's your doubt ?
 
BvU said:
Where's your doubt ?

What do you mean?
 
You post a picture of the question and you post a picture of your answer. Your question is: does it look correct?
Well, what if it does? Which parts are you confident about, which parts are somewhat less certain in your opinion?
 
Bedtime for me, but to help you on your way: perhaps the x3 isn't really there...: the wall on the right looks pretty solid.
 
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