8. Find the partial-fraction expansion to the following functions and then find them in the time...
Q3: Expand the following functions by partial fraction expansion. Do not evaluate coefficients or invert expressions. 2 (a) x(s) = (5 + 1)(²+1) (s +3) (6) X() – F76+ 16 + 24 g Dos (b) x(s) = 31 sºls + 1) (s + 2)(s + 3) (c) X(s) = 1 (s + 1)(s + 2)(8 + 3)(s + 4)
Find the time function corresponding to each of the following Laplace domain functions. Use the proper partial fraction expansion (PFE) when necessary then use the Laplace tables. 10 la 8(8 + 1)(8 + 10) 2s + 4 (b) F() = (8 + 1)(2+4) (C) 53 +352 +58 +8 (8) = (x + 1)(2 +9)(2+28 + 10) - Doozy.
8. Write out the form of the partial fraction expansion for the following transfer function. SOME FACTORING AND CANCELING MAY BE REQUIRED IF THE DENOMINATOR IS NOT IRREDUCIBLE G(s) = +4+46 +4+6) To get full credit you need to have the denominators correct and the form of the numer- ators correct. DO NOT solve for the values of the numerator coefficients. You don't need to for credit and it would take a long time. 8+2
The residue command can also be used to form polynomials from a partial fraction expansion. The command [N,D] = residue(r.p.k) converts the partial fraction expansion rp,k (defines as before) back into the polynomial ratio B(s)/A(s). Given a partial fraction expansion roots of -6, -4, and -3; poles as -3, -2,-1, and direct term 2 use MATLAB residue command to determine the numerator and denominator polynomial coefficients given as n1 [Choose) n2 [Choose] n3 [Choose ] 6 2 10 -8 11...
8. Write out the form of the partial fraction expansion for the following transfer function. SOME FACTORING AND CANCELING MAY BE REQUIRED IF THE DENOMINATOR IS NOT IRREDUCIBLE G(8) = +4+36 +4+6 To get full credit you need to have the denominators correct and the form of the numer- ators correct. DO NOT solve for the values of the numerator coefficients. You don't need to for credit and it would take a long time.
Partial Fraction Expansion (Case 4) 15 pts. Using Partial Fraction expansion find f). L-II F)]-fo). hint: The denominator factors into complex roots. 36 s2+16s + 100 s) =
Find the unknown constants, a1 and a2 in the partial fraction expansion 3 s + 15 ( s + 6 ) 2 = a 1 ( s + 6 ) 2 + a 2 ( s + 6 ) .
Use the method of completing the square to find the partial fraction expansion and inverse transform. F(s) = (s+4)/(s^3+4*s^2+s)
MATLAB c. Determine the Partial Fraction Expansion and the Laplace Inverse) of the following ace Inverse (fo)) of the following function F(s), using MATLAB: F( s) = (s+ 2) (s+ 4) (s + 6)2
Find the partial fraction expansion of the following Laplace domaim function 100 H (s)-s(10(s41) s (s2 +As+8) the inverse Laplace of H (s) to find h(t). Simply the expression as much as powsible.