Problem $3(30$ points $)$

For the system given in figure. Use elemental equations supplied in solution of Homework $2.$

a$.$ Consider $q_{mi}$ is input and $q_2$ is output and obtain the transfer function of the system. $(5$ points$)$

b$.$ Consider $q_{mi}$ is input, $P_3$ is output and obtain the transfer function of the system. $(5$ points$)$

c$.$ Obtain the full block diagram of the system. Consider $q_{mi}$ is input, $x$ is output. Use only elemental equations. Do not use any manipulated equations, nor reduce any blocks. $(20$ points$)$