Consider the mechanical systems shown on second page below. In the below table, you will see your

version and parameters of your system.

a$)$ Draw free body diagrams of each masses

b$)$ Write mathematical models $($Differential equations$)$ for each masses

c$)$ Obtain state$-$space model of the system.The input force f$1$ f$3$ and outputs are translations y$1,$ y$2,$ y$3$

m$1=12$ m$3=10$ k$1=17$ k$2=27$

k$3=37$ b$1=9$ b$2=10$

m$2=15$