Tutorial Laplace Transform1- Find the Laplace transform and the corresponding ROC of the followingsignals.a) x(t) = [e-2 + e' cos(3t)]u(t)b)x(t) = e-altl = e-atu(t) + eatu(-t) , consider a>0.c) x(t) = 8(t) + 8(t – 1) + 8(t – 2)d) x() %3D и(-1) - и(1)e) x(t) = e-3t Lo T sin(2t) u(t)dtf) x(t) = [r³ +sin(2t)]u(t)drg) x(t) = t2e-2t cos(5t) u(t - 1)2- Find the inverse of Laplace transforms-1, Re[s]>-3a)s2(s+3)s+5, i) Re[s]> 3 ii) Re[s]>-1 ii) Re[s]<3 iii) -1 1s+5d)(s-1)(s-2)(s-3)'i) Re[s]> 3 ii) Re[s]<1iii) 1 -3 ii) Re[s]<-1iii) -1>Re[s]> -3

Laplace transform and ROC of question 1(a,b,c).

1- Find the Laplace transform and the corresponding ROC of the following signals. a) x(t) = [e-2t + et cos(3t)]u(t) b)x(t) = e-altl = e-atu(t) + eatu(-t), consider a>0. c) x(t) = 8(t) + 8(t – 1) + 8(t - 2) %3D %3D ハ 1) u(1)

1- Find the Laplace transform and the corresponding ROC of the following signals. a) x(t) = [e-2t + et cos(3t)]u(t) b)x(t) = e-altl = e-atu(t) + eatu(-t), consider a>0. c) x(t) = 8(t) + 8(t – 1) + 8(t - 2) %3D %3D ハ 1) u(1)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

1. Compute the Fourier transform of the following signal: Plot the signal and x(t) = e-3t| sin(2t)u(t)
1. Find the Fourier transform of (a) f (x) = exp (-a.x²), (b) f (x) = exp (-a|x|), where a is a constant.
4) Find the Laplace Transform of the following functions: f(1) = Eu(t – n) n=0 f (t) = (-1)t/a] : [] denotes the greatest integer not exceeding x.
Obtain the Fourier transform of the double pulse defined by f(t) ={ 1 ,1< or equal to x < or equal to 2 f(t) = {0 , otherwise
Sketch the following waveform f(t)= Vo = 0 -t/2≤t≤t/2 otherwise and show that its Fourier transform is F (1) 2sin Varsine ( Votsinc (0) 2 ωτ Use this result to sketch a fully labelled graph of the amplitude spectrum of a single square voltage pulse, of amplitude 24V and pulse width 1.4μs, using units of Hz for the frequency axis. (Note: graph paper is not required - a clear, fully-labelled sketch is adequate).
5. Find the Fourier Transform of the given signal and plot its frequency spectrum. x(t) = 2 e u(-t)
Let Ibe the Laplace transform. Find (+ - Dř (s – 1)² + 4 A) E) + (sin t)e (C) + sin(2t) (D) + (sin t)U(t – 1) where U is the unit-step function. 4! + é" sin(2t) 4!
The percentage of female high school graduates who enrolled in college is given in the table below. Year 1970 1980 1990 2000 2010 College Enrollment Percentages for Females 25.5 30.3 38.3 45.6 50.5 Let a represent time (in years) since 1970, and let y represent the corresponding percentage of female high school graduates who enrolled in college. Find the cubic regression model y = F(x) = ax³ + bx² + cx + d, = where a is rounded to 6 decimal places, b is rounded to 4 decimal places, c is rounded to 3 decimal places, and d is rounded to 1 decimal place.