Answer Happy

Hi please help with number 4 if possible
с TO R С HE R w R + Vin V 3 tv2 For the summer in the above circuit it can be proved that 2R2 2R1 Vi = Vin + R1+R2 V2 - V3 R1+R2 (2) = ....... (3) and from developing the transfer function, it can be proved that R RC R1+R2 In the laboratory, you will be provided with a breadboard version of the above electronic system with Wn= 482 Hz (R = 33 kN and C = 0.01 uF) R1 = 22k12 3. PRE-PRACTICAL WORK 3.1. Derive the relationship between V2 and V. [5] 3.2. Derive the relationship between V3 and V1. [5] V3(s) 3.3 Obtain the transfer function of the amplifier, given by G(s) = Vin(s) [5] of the 3.4 Show that, with the use of the relationships in equation (3), the transfer function amplifier could be written as G(S) = s2+28Wns+w [5] K 3.5 Select a value of R1 to yield an under-damped system (damping factor in the range 0.1515 0.5). Calculate the value of R2 corresponding to the damping factor you have chosen. Evaluate mathematically and tabulate the phase and magnitude frequency responses of the under-damped system. [5] 3.6. Select a value of R1 to yield an over-damped system (damping factor in the range 0.7</s 0.9). Calculate the value of R2 corresponding to the damping factor you have chosen. Evaluate mathematically, and tabulate the phase and magnitude frequency responses of the over-damped system. [5] Resistor values available for use are: 2.7kΩ; 5,6kΩ; 10kΩ; 22kΩ 56kΩ; 100kΩ; 180kΩ 4 SIMULATED PRACTICAL WORK 4.1 Using the MATLAB/Simulink environment, implement G(s) for the under-damped system. Connect a sine-wave generator to the input of the system. Connect the V3 output voltage to a source (or sources) that would enable the measurement of the magnitude and phase of V3 set the value of the input voltage to 5V. Vary the frequency of the input sinewave source in steps, from 0.1Hz and 200Hz. Tabulate the frequencies used in radians/sec (w), the values of V3 (V) and phase-angle (degree). [15] 4.2 Using the MATLAB/Simulink environment, implement G(s) for the over-damped system. Connect a sine-wave generator to the input of the system. Connect the V3 output voltage to a source (or sources) that would enable the measurement of the magnitude and phase of V3: set the value of the input voltage to 5V. Vary the frequency of the input sinewave source in steps, from 0.1Hz and 200Hz. Tabulate the frequencies used in radians/sec (w), the values of V3 (V) and phase-angle (0(degree). [15]