Problem SOu ponts Calculate the Laplace transform of the signal given below using 2.5 2 1.5...
What is the Laplace Transform of below function ? 0.5 o 0.5 1 1.5 2 2.5 3 Time (s) 3.5 4 4.5 5 5.5 Cae-1.551 0.51 s? +(0.571)2 40 OB.( OB. (5-1.5)2 + (410) 0.571 OC (3–1,+0.50 00.2-15742 m OE. None of above
Q3. There exists a signal f(t) whose Laplace Transform has the following poles Pole-Zero Map 093 087 0.78 064 0.8 0 97 0.6 0.40 99a 0.2 25 1.5 05 20.2 0.4 0.92 0.6 097 0.8 093 087 078 064 2.5 1.5 0.5 Real Axis (seconds) e2tf(t) and P(jo) converges. Decide whether f(t) is right sided/left Another function p(t) sided/ 2 sided. Justify your answer clearly. Hint: P(ja) refers to Fourier Transform of p(t) Q3. There exists a signal f(t) whose...
Express the function below using window and step functions and compute its Laplace transform. 0, 0<t<3 2, 3<t<5 g(t) = 6, 5<t<8 4, 8<t 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. O A. g(t) = 2ut - 3) + 6(t-5) + 4u(t-8) B. g(t) = 2113,5(t) + 6115,8(t) + 4u(t-8) O c. g(t) = 2113,5(t)...
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)...
Laplace Transform Problem 3. (15 points) Given f(t) = 4e-2tu(t) + 29u(-t) a) Using the Laplace Transform table 9.2 find the bilinear Laplace transform, F($) and sketch the region of convergence (ROC) in the s-plane showing all poles. State the ROC as an inequality. b) Another function is added so that fa(t) = 4e-2tu(t) + 7u(-t) – 10e-10t u(-t). Find the Bilinear Laplace Transform of fa(t) and sketch the region of convergence in s-plane also showing all the poles. State...
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....
2. Given 12 f(t)= ={ Ost<3 t23 (a) Write f(t) in one line using the unit step function (Heaviside function). 5 points 10 points (b) Find L{f(t)}, either by using the definition of the Laplace transform or by finding the Laplace transform of your answer to part (a).
Problem #9: The graph of f(t) is given below. 5 4 3 2 2 10 4 -1 1 (a) f() can be represented using the following combination of Heaviside step functions а U(t - 3) + b U(t - 4) + с U(t - 9) Enter the constants a, b, and c (in that order) into the answer box below. (b) Find the Laplace transform F(s) = Pf()} for s 0. a, b, c (in that order), separated with commas....
(II) USING THE LAPLACE TRANSFORM TO SOLVE DIFFERENTIAL EQUATIONS PROBLEM 1: (A practical example with repeated poles) A car of mass M and friction coefficient Kris stopped at a red traffic light (initial position and initial speed are zero). At 1-0, when the light turns green, a unit-step input force u(t) is applied to the car. In this problem, we are interested in the car position(0); not the car speed. (30 points) Find the car transfer function Y(s)y U(s). Find...
Problem 2 (20 points) Let (2t +1, Ostsi x() +4 st 3 be a periodic signal with fundamental period T=3 and Fourier coefficients ar. a. Determine the value of an b. Determine ax, k 0, by: 1.first finding the Fourier coefficients of CID II.then using the appropriate property of the continuous-time Fourier series. c. Use the result of part(b) to express the Fourier transform of (t).