9.21. Determine the Laplace transform and the associated region of convergence and pole- zero plot for each of the following functions of time: (a) x(t) = e21 u(t) + e −31 u(t) == (c) x(t) = e²u(t) + e³¹ u(t) te-21 (e) x(t) ====== (g) x(t) = { 1, 0 ≤t ≤1 0, elsewhere (i) x(t) = 8(t) + u(t) (b) x(t) = et u(t) + est (sin 5t)u(t) (d) x(t) = te-2|1| (f) x(t) == (h) x(t) = { (j) x(t) = teu(-1) t, 2 0 ≤ t≤ 1 - t, 1 ≤ i ≤ 2 8(31) + u(31)

Express the function below using window and step functions and compute its Laplace transform. 2190 Q 0- 5x 16 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. Express g(t) using window and step functions. Choose the correct answer below. A. g(t)= (sin 8t)u t-- (sin 8t)u (1-56) OB. 9(t)=11 sin (81) OC, 9(t) = (sin 8t)II 5x (t) + (sin 8t)u t- 0.7 16 salt) 0.16 I OD. g(t)=(cos 8t)u t-- : 8tu (1-556) 16 Compute the Laplace transform of g(t). L(g) = (Type an expression using s as the variable.)

Q1 Find the z transform for each of the following sequences: a) 3u(n-4) b) 2(-0.5)nu(n) c) 4e-2nu(n) d) 4(0.8) "cos (0.1лn)u(n) Q2 Given the two sequences x₁(n)= -28(n)+58(n-2) and x2(n)= 48(n-4) a) Let x3(n) = x₁(n) * x2 (n) Determine the Z transform of x3(n) b) Find x3(n) using the inverse transform of X3(z). Q3 Using the Z-transform properties and the Z-transform table find the inverse Z- transform for each of the following sequences a) 5- (7z/z+1) - (3z/z-0.5) b) (-3z/(z-0.5)) +[ 8z/(z−0.8)]+ [2z/(z-0.8)²] c) 3z/(z²+1.414z+1) d) (5z %/z-1)-[ z^²/(z−1)²] + [z −¹⁰0] + [z ³/z-0.75] Q4 Use partial fraction expansion, Find the inverse Z-transform of the following: a) [1/(z²+0.5z+0.06)] b) z/[(z+0.3)(z-0.5)] c) 5z/[(z-0.75) (z²-z+0.5)] d) 2z(z-0.4)/[(z-0.2)²(z+0.8)] Q5 A system is described by the following difference equation y(n)-0.5y(n-1) +0.06y(n-2)= (0.4)n-1u(n-1) Determine the solution when the initial conditions are y(-1) = 1 and y(-2)=2.

Note:- You are attempting question 5 out of 12 The final value or steady state value of the following system using the concept of final value theorem of Laplace transform for a unit step input is, 6+ (a) 0 (c) 0 (d) Can't be determined Answer A Su realme Shot by Gowthamnag 2021/10/30 12:20