Question: Conditions of stability with TableRouth and Solving inequations


I could build the table routh of the characteristic equation of the system by using the function RouthTable( )

I try to find the stability conditions as fonction as the gain g. For that purpose, i have to solve some inequalities.

Each terms of the first column of the routh table should be positive.

I would like to find the conditions on the gain g so that my system is stable.

In order to solve the inequalities as function of g, i must assume the mass, and the spring to be positive. I'm not sure that i have well assumed the parameters to be positive.

Have you some ideas to solve my inequalities and find symbolically the conditions of the gain g? 

I attach an extract of my code.

Thank you for your help

Extract of my code:



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