(Solved): Q3 (40 points): An RLC Circuit is shown below: (a) Obtain the differential equation of this RLC ci ...

Q3 (40 points): An RLC Circuit is shown below: (a) Obtain the differential equation of this RLC circuit (Hint: you can use KVL to obtain this differential equation). (10 points) (b) Identify a suitable set of state variables and write the state space model (Hint: you need 2 states to write the state-space representation). (10 points) (c) Define the input \( u(t)=v(t) \) and the output \( y(t)=v_{c}(t) \). Calculate the transfer function \( Y(s) / U(s) \) using the state equations (Hint: \( \left.\frac{Y(s)}{U(s)}=C(s I-A)^{-1} B+D\right) \cdot(20 \) points)