Base excited stacked mass spring damper systems

[QuantumLollipop]

Homework Statement

I'm trying to derive the equations of motion and state space as well as the transfer function for a system which has two mass spring damper systems stacked on top of each other. The system is base excited. I attached a pic of the system

Homework Equations

- Sum of the forces as per usual
- The transfer function is defined as H(s)=X(s)/U(s)

The Attempt at a Solution

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And setting up for state space:

I've also been thinking this might be easier in terms of energy methods. Thanks in advance

 

[rude man]

Your equations look right. You can solve by the usual diff. eq. methods.

There is probably limited knowledge base on this forum for state space. I took an entire course in state space techniques (my instructor, Prof. S. C. Gupta, had us check his answers in the textbook he was preparing; maybe you know it) but I have to say I never found the technique useful to me so forgot all about it.)