Find the transfer function of the following system G(s) = IR(s) Ii(s). (20 Points)Assume L = 1 H and C = 4 F. (40 Points) a) Find the values of R that generates different system responses to the unit step input such as "overdamped, underdamped, critically damped and undamped". (10 Points) b) Define the corresponding transfer function, of previous part, in MATLAB for each case. (10 Points) c) For each case, plot pole and zero locations and step system response of the system in a single figure using subplot. (10 Points) d) Redo the simulation in MATLAB Simulink and show the results in a scope. (10 Points)
![For the circuits shown: 1. a) Derive the s-domain transfer function, [10 points] 2. b) Using bode approximations (straight-line), plot by hand both the magnitude and phase response of the transfer function. Use the semilog template posted below. [10 points] 3. c) Plot the magnitude and phase of the transfer function in either Python or Matlab. Include the code used to generate the plots. [10 points] 4. d) Simulate the magnitude and phase response using Multisim. [10 points] 5. e) Report the values for DC gain, gain at infinite frequency, the location of poles and zeros for each transfer function, and indicate whether the circuit is a low-pass, high-pass, or band-pass filter. [10 points] Hint: s = jω = j2πf, where f = frequency in Hz (cycles/second) and ω = angular frequency in rad/sec](https://www.doubtrix.com/uploads/editor/9811588259hyaBapTrMi.png)
