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I am taking a course in dynamics and have a question about a spring-mass-damper system (see the attached file) that I want to solve using Lagrange equation (see attached file).

I am having trouble writing the equation of motion for this problem. At first I tried doing it the way I would for a system with two masses, connected by springs and dampers. This gave me a system of equations which I then used the State Space Approach on. I set the first mass=0, only to realize that I would not be able to get the homogenous solution this way.

Any help is appreciated! Thank you very much!

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# Mass Spring Damper system

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