Robotics Control System

A system is observable if:
(i) States can be measured from outputs
(ii) Inputs are visible
(iii) Poles are real
(iv) Transfer function exists

Why are electrical analogies used in control systems?
(i) For heating purposes
(ii) To make the system unstable
(iii) For simplified modeling
(iv) To avoid complexity

For system $A = \begin{bmatrix} 0 & 1 \\ -1 & -3 \end{bmatrix}$, $B = \begin{bmatrix} 0 \\ 1 \end{bmatrix}$, check controllability using rank.
(i) Rank = 2, controllable
(ii) Rank = 1, uncontrollable
(iii) Rank = 2, not observable
(iv) Rank = 1, observable

The SFG of a control system is shown in the figure below. Find the transfer function $C/R$.

Consider the mechanical system shown in the figure below. Find the transfer function $G(s) = \frac{V_1(s)}{F(s)}$