Q3: Expand the following functions by partial fraction expansion. Do not evaluate coefficients or invert expressions....
8. Find the partial-fraction expansion to the following functions and then find them in the time domain. (Homework) 100s +1) (a) G(S) 215 + 4)(8+6) (s +1) (b) G(s) = 5(5+2)(52 +28 +2) 5(s + 2) 52(+ 1)(8 + 5)
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(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
1). Perform partial fraction expansion on the following Laplace Transform expressions a) s2+3s +2 2). Solve the following differential equations x(0)-0(0)-0
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.
2. Expand the following f) into partial fraction: 4.x 3 +16x2 +23x +13 a r + 2) the following fts into partial fraction: (ar t 1 (e 4 2) 152 f(x)- Find a,, a, and b.
Finally, we now mention MATLAB commands that can be used to help in the partial fraction decomposition of rational functions. This can be used when we need to express the Laplace transform as a partial fraction and then using a table and uniqueness property of the Laplace transform derive the time function. First, lookup how the commands collect and expand work. Now, read up on the documentation of command [x,p,k]=residue (b, a) to answer the following questions. Lab Exercise 1....
Evaluate the following expressions, given functions f, g, and h: f(x) = 9 – x2 g(x) = –2x² + 5x +8 h(x) = 2x – 5 a. 4f(3) – 28(-2) = -10 b.f (!) – h(-3) =
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 ) .
Perform inverse Z of the following partial fraction expansion using Table 5.1 (note: you are directly using the table, mention which properties are used to do the inverse): [6 pts] presion using Table si come your phone - 2zz Y[z] = (2-0.6)* + 22 - 62 + 25 (-22 + 16) For the given periodic series, computer T, W., and write the integral for finding an with proper signal amplitudes, and limits, between intervals -2 and 2. Don't solve. [4...