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

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SUMMARY

The discussion focuses on the formulation of two second-order ordinary differential equations for a mass-spring-damper system. Participants analyze the correctness of the equations presented by the original poster, emphasizing the need for clarity regarding specific components, such as the presence of the x3 term. The conversation highlights the importance of understanding the physical setup and constraints of the system to ensure accurate modeling.

PREREQUISITES
  • Understanding of second-order ordinary differential equations
  • Familiarity with mass-spring-damper system dynamics
  • Knowledge of free-body diagram interpretation
  • Basic principles of mechanical systems and forces
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  • Study the derivation of equations for mass-spring-damper systems
  • Learn about free-body diagram techniques in mechanical engineering
  • Explore numerical methods for solving ordinary differential equations
  • Investigate the impact of boundary conditions on system behavior
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Students and professionals in mechanical engineering, physics enthusiasts, and anyone involved in modeling dynamic systems will benefit from this discussion.

kal854
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Problem: Write the equations as a set of two, second-order ordinary differential equations.

2d5a81.jpg



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

dz8m0n.jpg
 
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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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