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 + 0.2
π
).
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)].