The transfer functions are given such that (S+12) a. Ti(s) = 33+2+ 2(5+1)(s2+28+3) b. T2(s) = 54 +353 +592 +5-10 (s2+35+5) C. T3(s) 53+52 +s+6 (552 +4s+1) d. T4(s) = 53+52 +4s i. Analytically, find the partial fraction expansion and find the Inverse Laplace Transform of T(s). (Hint: use MATLAB to find the roots of the function.) For example : find th roots of the poynomial r(s) = s3 + 5s2 + 12 = 93 +592 + 0 s + 12s MATLAB Command window : r = [1 5 0 12] roots(r) ans: -5.4100+ 0.0000i (real root) 0.2050 + 1.4752i (complex root) 0.2050 - 1.4752i (complex root) ii. Find the Inverse Laplace Transform of functions using MATLAB. (Hint: use ilaplace command.) The transfer functions are given such that (S+12) a. Ti(s) = 33+2+ 2(5+1)(s2+28+3) b. T2(s) = 54 +353 +592 +5-10 (s2+35+5) C. T3(s) 53+52 +s+6 (552 +4s+1) d. T4(s) = 53+52 +4s i. Analytically, find the partial fraction expansion and find the Inverse Laplace Transform of T(s). (Hint: use MATLAB to find the roots of the function.) For example : find th roots of the poynomial r(s) = s3 + 5s2 + 12 = 93 +592 + 0 s + 12s MATLAB Command window : r = [1 5 0 12] roots(r) ans: -5.4100+ 0.0000i (real root) 0.2050 + 1.4752i (complex root) 0.2050 - 1.4752i (complex root) ii. Find the Inverse Laplace Transform of functions using MATLAB. (Hint: use ilaplace command.)