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Engineering Analysis Q.1. f(t) = {S; if - 4 <t<o if 0 st <4 a) Sketch...
Find the Laplace transform of the function f(t). f(t) = sint if o St<$21; f(t) = 0 if t> 21 Click the icon to view a short table of Laplace transforms. F(S) =
Find the Laplace transform of the function f(t). f(t) = sint if 0 St< $41; f(t) = 0 ift> 41 Click the icon to view a short table of Laplace transforms. F(s)=
Consider the function f(x) with period 4 which has f(x) = 1, -2<< -1, 0, -1<x< 1, -1, 1<x< 2. a) Sketch the function f(x) in the interval (-2,2] b) Calculate the Fourier Series for f(x). Circle your answer. c) What values does the series converge at the points x=-1 and x=1. Circle your answer.
Find the Laplace transform F(s) - {0} of the function: f(t) = 1-21 0314 2-34 4 <t<6 14 6 by splitting the integral into three pieces. Enter your answers in order of increasing domain.
Problem 1. x(t) = 2 cos(210.8t) + 3cos(270.2t) 1) Sketch x(t) for 0<t<2 2) Find the Fourier Series coefficients for x(t)
Also : FS (2.8) FS (4) FS (5) The function f(t) is defined by -3t+6, 0<t<4 f(t) = -3, 4 < t < 5. Let f (t) denote the periodic extension of f(t), with period 5. Evaluate f (-2.3), f (O), f (7.5), f (9.2) and state the value to which the Fourier series of f (t), FS(t), converges for each of the following values: t = 0,t = 2.8, t = 4, t = 5. Enter all your answers...
Find the required Fourier Series for the given function f(x). Sketch the graph of f(x) for three periods. Write out the first five nonzero terms of the Fourier Series. cosine series, period 4 f(0) = 3 if 0<x<1, if 1<x<2 1,
(t) = 0 <t< dz W sint - 4) If 4 st. a. Use the graph of this function to write it in terms of the Heaviside function Use hit-a) for the Heavis de function shifted a units horizontaly f(t)- help (formulas) b. Find the Laplace transform F(x) = ()} FC) - 40) help (formulas) Note: You can earn partial credit on this problem
3. Consider the function f(t) = ' π2 , with f(t) = f(t +2r). 0<t<π (a) Sketch f(t) by hand for-3r < t < 3T. (b) Determine the general Fourier Series for f(t). (c) Use MATLAB to plot f(t) and the n = 4 Fourier series representation on the same set of axes for -t<T
Consider the following. 1, -LSX<0. 10. OSX<L; f(x + 2) = f(x) (a) Sketch the graph of the given function for three periods. (In these graphs, L = 1.) f(x) — — - - - 1 -3 -2 -1 1 2 -3 3 3 -2 -1 . 2 1 (b) Find the Fourier series for the given function. R0 - 4 - ŠOx)