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Piecewise function f(t) = 1 when 0 < t < 1, and f(t) =-1 when-1 <...
Problem 3. Given: f(t) 3 -22 f(t) 0 otherwise 3.1 Determine which one of the following expressions is the (a) (1.5jw) (ee (b) (3/jw) (e -e Fourier transform for f: jw -jw jw) (e e 1.5jw 1.5jw (d) Bjw) (e (e) (2jw) (ee) 3.2 Rewrite F(w) as as a trigonometric sinusoidal function and sketch its wavefom. 3.3 Determine the values of first two frequency terms (w1 and w2) where F(w)-0. 3.4 Determine the inverse Fourier transform of f(t) and sketch...
The Laplace transform of the piecewise continuous function $4, 0<t<3 f(t) is given by 2, t> 3 1 L{f} (1 – 2e-st), 8 >0. S None of them L{f} = (1 – 3e®), s>0. 2 L{f} (3 - e-), 8 >0. S 2 L{f} (2-est), s >0. S
The Laplace transform of the piecewise continuous function $4, 0<t<3 f(t) is given by 2, t> 3 1 L{f} (1 – 2e-st), 8 >0. S None of them L{f} = (1 – 3e®), s>0. 2 L{f} (3 - e-), 8 >0. S 2 L{f} (2-est), s >0. S
Question 9 3 pts The Laplace transform of the piecewise continuous function 4, 0<t <3 f(t) is given by t> 3 (2, L{f} = { (1 – 3e-*), s>0. O 2 L{f} (2 - e-st), 8 >0. 2 L{f} = (3 - e-st), s >0. O None of them 1 L{f} (1 – 2e -st), s >0.
0and / is an odd function of t, find the Fourier sine sin wt d for 0<t< 1 10, (a) If f(t) = for t a 0 transform of f. Deduce thato s if0<t < a. What is the value of the integral for t2 a? for 0 < t < b (b) If g(t)-{ b-t and g is an even function of t, find the Fourier 0 cosine transform of g. Deduce that foo 1-w2bw cosa t dw =...
0<t<T when Tt< 2 t 2T sin t when 2. Calculate the Laplace transform of the periodic function f(t) 0 f(t-2) when -7s 3. Calculate the inverse Laplace transform of G(s) 3-4e-5 + $2+2s+17 4. Use the Laplace transform to solve each initial value problem: 4y"+ y u2m(t)sin(t/2) y(0)=0 &(0 =0 (a) 0 and /(0) 2 "+4y+13y = 4to(t-T) if y(0) (b) 5. Use the convolution to write a solution of each initial value problem. y"+6y'+10y g(t) 1 y(0) 0...
Need solution pls... 2. Find the Fourier transform of f() = {6 1 – 12 \t <1 1t| > 1 Use the first shift theorem to deduce the Fourier transforms of e3jt (1-12) 11 <1 (a) g(t) 1t| > 1 {" (b)h() = {**"1 –1) "151 It| > 1 Answer: 63 4 cos o 4 sin o + -62 -4 cos(w – 3) (a) (0 – 3)2 -4 cos(w – j) (b) (w – j)2 + 4 sin(0 – 3)...
Sketch a graph of the piecewise defined function. sz if x <3 f(x) = x 1 if x 2 3
Rewrite the following piecewise continuous function f (t) in terms of the unit-step function. Then find its Laplace transform f(t) = Rewrite the following piecewise continuous function f (t) in terms of the unit-step function. Then find its Laplace transform f(t) =
f(t) F(S) (s > 0) S (s > 0) n! t" ( no) (s > 0) 5+1 T(a + 1) 1a (a > -1) (s > 0) $4+1 (s > 0) S-a 1. Let f(t) be a function on [0,-). Find the Laplace transform using the definition of the following functions: a. X(t) = 7t2 b. flt) 13t+18 2. Use the table to thexight to find the Laplace transform of the following function. a. f(t)=t-4e2t b. f(t) = (5 +t)2...