Laplace Transforms Problem Set for EE 223, April 2003, Assignments of Microelectronic Circuits

Download Laplace Transforms Problem Set for EE 223, April 2003 and more Assignments Microelectronic Circuits in PDF only on Docsity! Problem set #11, EE 223, 4/22/2003 – 4/29/2003 Chapter 14, Problem 13. Use Eq. [14] to find the Laplace transform of the following: (a)2 +3u(t); (b) 3e –8t ; (c) u(-t); (d) K , where K is an unknown real constant. Eq. [14] Chapter 14, Problem 17. For each of the following functions, determine the one-sided Laplace transform: (a) 8e-2t[u(t + 3) - u(t – 3)]; (b) 8e2t[u(t + 3) - u(t – 3)]; (c) 8-2 |t|[u(t + 3) - u(t – 3)]. Chapter 14, Problem 22. Evaluate the following: (a) 8 sin 5t δ(t – 1)dt; (b) (t - 5)2δ(t – 2)dt; (c) Kδ(t – 2)dt, where K is a real constant. Chapter 14, Problem 23. Use the definition of the (one-sided) Laplace transform to find F(s) if f(t) equals (a) [u(5 - t)][u(t – 2)]u(t); (b) 4u(t – 2); (c) 4e-3tu(t – 2); (d) 4δ(t – 2); (e) 5δ(t) sin(10t + 0.2π). Chapter 14, Problem 26. Find the inverse transform of each of the following without performing any integrations and without resorting to the use of MATLAB: (a) 5s-1 - 16 + (s +4.4)-1; (b) 1 – s-1 + s-2; (c) 5(s + 7)-1 + 88s Chapter 14, Problem 31. Given the following expressions for F(s), find f(t): (a) 5/(s+1); (b) 5/(s+1) –2/(s+4); (c) 18/[(s+1)(s +4)]; (d) 18s/[(s+1)(s+4)]; (e) 18s2/[(s+1)(s+4)].