Consider the object on the table with air resistance (6-17), friction (k=8) and mass (m=2), F F Mon Figure 1 the object on the table a) (10P) Drive the differential equation of the system and transfer it in Laplace Domain, b) (5P) Consider the equation you found in question (1a) and add something that makes the gain of the equation unity, c) (10P) Reduce the order of the system that you have found in equation (1b) into first order, d) 10P Plot and compare the system that you have derived in the question '1b' and '1c (Hint: the gain of each system should be unity), e) (SP) Draw the closed loop block diagram with Cs()= +ks ka p f) (10P) Derive the closed loop transfer function that you have found in equations (1b) and (1c) for controller, g) (15P) According to the transfer function in question '1b' and the equation that you have derived closed loop transfer function in question (1f) due to the transfer function in 1b', design a controller using pen and paper that the damping ratio (V) of the closed loop transfer function will be 0.2 (Calculate by yourself, do not use MATLAB). h) (10P) Plot the closed loop response and check that the damping ratio of the closed loop system is meet in question (1g). 1) (15P) According to the transfer function in question '1c' and the equation that you have derived closed loop transfer function in question (1f) due to the transfer function in *1c", design a controller using pen and paper that the damping ratio (V) of the closed loop transfer function will be 0.4 (Calculate by yourself, do not use MATLAB). j) (10P) Plot the closed loop response and check that the damping ratio of the closed loop system is meet in question (11).