Objective: This activity has the purpose of helping students to plot common signals, perform a Partial Fraction Expansion, calculate the Pole-Zero Plot of a system Transfer Function in the S Plane and calculate the Inverse Laplace Transform Objectives 1.4.5.6. Student Instructions: Discussion Board activity 0 points 0% Can be completed after completing Subtheme 5 Given the following rational expression, which has repeated quadratic factors Y(s)- s + 5s +12s +7s +15 (s+ 2)(²+1) Use the MATLAB symbolic toolbox to find an analytical expression for the Inverse Laplace Transform, y & Use MATLAB to plot the inverse transform, y(t) based on the result in part a Use MATLAB to obtain the pole-zero plot for Y(s) Use MATLAB and the residue command to perform a partial fraction expansion on Y(s) Perform at least two of the following activities Activity 1 is mandatory and then select at least one of activities 2.3 and 4 1 Post in the discussion board your solutions/methodology to at least two of the (ab.c.d) parts of the proposed exercise 2 Post asking for help from your peers regarding how to solve this exercise or how to troubleshoot any problems confronted with MATLAB 1 Post you answer to any student questions regarding this exercise and/or MATLAB 4 Post any appropriate conections to other student posts