If Gc ( s ) G ( s )= 1 s3 + ( 1+k ) s2 +3 s+(1+ 4 k) and H ( s ) =1 a. Find the bounds of k to maintain the stability of the system using the Routh Hurwitz Criterion. b. Plot the step response of the system for the marginally stable values of k found in a). If the plot tends to infinity either increment or decrement the value of k by 0.0001 to produce a bounded plot. c. For the bounds of k found in a) plot the pole locations corresponding to a marginally stable system. Plot all pole locations together on the same plot. Include a legend to differentiate which set of poles correspond to the specific k values. d. Comment on how the stability and/or marginal stability of the system depends upon the value of k. e. Plot the pole locations of system for k=-5 : 0.01 : 3