



F(s), (10 points: 5+5) Obtain the Laplace transform for each of the functions given below. ĢIT when the Laplace transfo...
Obtain the Laplace transform of the functions plotted in Figures
1 and 2.
Obtain the Laplace transform of the functions plotted in Figures 1 and 2. ft) f(t) 14 0 10 20 30 40 Figure 1 Figure 2
Do: Find the Laplace transform, F(s), for each f(t) given below in parts a) and b). Express F(s) polynomials ins where the denominator polynomial, A(s) Le., it has the value "1" (one) Monic Rational Form (MRF). This means that the result is a ratio of polynomials, and the coefficient, a, in the denominator polynomial, A(s) below is a, 1 as a ratio of =s"+a-1s"- + a28 +a1s +a0, is monic as the leading coefficient on the highest power of s....
Find the inverse Laplace transform of each of the following functions. a. F(s) = 4652 + 4) f(t) = c++{F(s)}(€) = [" 58 b. G(s) = 7 (s – 5)2(52 +36) g(t) = £•*{F(0)}(€) = *
3.5 Determine the Laplace transform of each of the following functions by applying the properties given in Tables 3-1 and 3-2. (a) xi(t) = 16e-2t cos 4t u(t) (b) x2(t) = 20te-21 sin 4t u(t) (c) x3(t) = 10e-34 u(t – 4) Table 3-1: Properties of the Laplace transform for causal functions; i.e., x(t) = 0 for t < 0. Property x(t) 1. Multiplication by constant K x(t) 2. Linearity K1 xi(t) + K2 x2(t) X($) = L[x(t)] K X(s)...
Write the function in terms of unit step functions. Find the Laplace transform of the given function. f(t) = {3, Ost<5 1-4, t> 5 F(s) = Need Help? Read It Watch It Talk to a Tutor
Write the function in terms of unit step functions. Find the Laplace transform of the given function. -(2 5, (-4, 0 st 7 f(t) = t 2 7 F(s)
Problem 2 (3 points) Given the unilateral Laplace transform of the impulse response for a causal system H(s) Determine h(t) the impulse response? Hint synthetic division! (s+10) 40 t-10 Problem 3 a) (2 points) What is the initial value of time function f(t) corresponding to the one sided Laplace Transform F(s) = (i.e. f(t) is causal) s(s+10)(2+4) lim f(t) = 0 40 lim f(t) = 1. t-0 10 x 4 lim f(t) = 0 t-0 lim f(t) cannot be computed...
Find the inverse Laplace transform of each of the following functions. a. F(s) = 5 $4(s2 + 4) t f(t) = 2*4{F($)}(6) = dw b. G(s) = 4s (s + 5)2( 32 +81) g(t) = •{F()}(t) = dw
(1 point) S 3, 0<t< 1 =10, 1st<2 Find the Laplace transform F(s) of the periodic function f(t) = with f(t + 2) = f(t) whose graph is given below. What is the minimal period T for the function f(t): T = e-st f(t) dt F(s) = (1 – e-Ts) 1.8 1.0
Signal and Systems
Problem 2 (3 points) Given the unilateral Laplace transform of the impulse response for a causal system H(s) Determine h(t) the impulse response? Hint synthetic division! (s+10) 40 t-10 Problem 3 a) (2 points) What is the initial value of time function f(t) corresponding to the one sided Laplace Transform F(s) = (i.e. f(t) is causal) s(s+10)(2+4) lim f(t) = 0 40 lim f(t) = 1. t-0 10 x 4 lim f(t) = 0 t-0 lim f(t)...