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

[kal854]

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

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

 

[BvU]

Where's your doubt ?

 

[kal854]

Where's your doubt ?

What do you mean?

 

[BvU]

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?

 

[BvU]

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.