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9. (a) Use the Tables of Fourier transforms, along with the operational theorems, to find the...
Answers are: 9. (a) Use the Tables of Fourier transforms, along with the operational theorems, to find the inverse Fourier transform of iw 4 + 9 w2 9 w2 (b) The function f(t) satisfies the integral equation: OO -4u Н(u) du + 6sgn(t) е З, f(t) 0- ft - u) е" = 4 e -OO Find the Fourier transform of the function f(t) and hence find the solution f(t) 7 "(1-)н, (b) Transform the equation by using the convolution Theorem:...
9. (a) Use the Tables of Fourier transforms, along with the operational theorems, to find the inverse Fourier transform of iw 45iw(iw2 (b) The function f(t) satisfies the integral equation: f(t)2 f(t - u) sgn(u) du — 6е" H(). Find the Fourier transform of the function f (t) and hence find the solution f(t) The sign function sgn(t) = 1 if t 0, 0 if t 0 and -1 if t < 0 H(t) is the Heaviside unit step function...
8. (a) Use the Tables of Fourier transforms, along with the operational theorems, to find the inverse Fourier transform of 1 12 8iw w2 _ (b) Hence, determine the inverse Fourier transform of -iw 12 8iw -w2' (c) Use Fourier transforms to solve d2y ,dy + dt2 12y (t 1 8 8. (a) Use the Tables of Fourier transforms, along with the operational theorems, to find the inverse Fourier transform of 1 12 8iw w2 _ (b) Hence, determine the...
6. (a) Use the Tables of Fourier transforms, along with the operational theorems, to find the Fourier transform of -3t e sin (2(t5) H(t5) (b) Hence, find the Fourier transform of 6 e-3t-it sin (2(t +5)) H(t+5). 6. (a) Use the Tables of Fourier transforms, along with the operational theorems, to find the Fourier transform of -3t e sin (2(t5) H(t5) (b) Hence, find the Fourier transform of 6 e-3t-it sin (2(t +5)) H(t+5).
Answers are: 10. (a) Use the Tables of Fourier transforms, along with the operational theorems, to find the inverse Fourier transform of 40 w2 - 13iw (b) Use Fourier transforms to solve dy -5t + 8y — 9е эH (). dt 15t H(t) 1 8t (а) (1) Н, 9 Then solve for 5iw (b) Apply the Formula of transform of derivatives to get: (iw+8)Y(w) Y (w) and take the inverse transform to have -8t у(0) — Зе 5 н(t) —...
7. (a) Use the Tables of Fourier transforms, along with the operational theorems, to find the Fourier transform of -3t e H(t 4) (b) Hence find the Fourier transform of -6 е б-3)е н(t — 4)
8. (a) Use the Tables of Fourier transforms, along with the operational theorems, to find the Fourier transform of sgn(t 1)e4t-1| (b) Hence, find the Fourier transform of 5i sgn(t 1) eit-4e-1| (Simplify your answer. 8. (a) Use the Tables of Fourier transforms, along with the operational theorems, to find the Fourier transform of sgn(t 1)e4t-1| (b) Hence, find the Fourier transform of 5i sgn(t 1) eit-4e-1| (Simplify your answer.
1. (a) Using the Tables of Laplace transforms, along with the operational theorems, de- termine the inverse Laplace transform of s +3 82 6s 16 (b) Hence deduce the inverse Laplace transform of 83 -6s e s2 6s 16 1. (a) Using the Tables of Laplace transforms, along with the operational theorems, de- termine the inverse Laplace transform of s +3 82 6s 16 (b) Hence deduce the inverse Laplace transform of 83 -6s e s2 6s 16
1. (a) Using the Tables of Laplace transforms, along with the operational theorems, de- termine the inverse Laplace transform of 3s 7 82 -2s + 10 (b) Hence determine the inverse Laplace transform of 3s +7 -2s S2-2s10 1. (a) Using the Tables of Laplace transforms, along with the operational theorems, de- termine the inverse Laplace transform of 3s 7 82 -2s + 10 (b) Hence determine the inverse Laplace transform of 3s +7 -2s S2-2s10
thank you for the help :) Question Question 17 (2 marks) Attempt 1 f(t) satisfies the integral equation: f(t)-5 | f(t-u) e-liu H(u) du=12 sgn(t-2) Find the solution of the integral equation using Fourier transforms. Your answer should be expressed as a function of t using the correct syntax f() Skipped Question Question 17 (2 marks) Attempt 1 f(t) satisfies the integral equation: f(t)-5 | f(t-u) e-liu H(u) du=12 sgn(t-2) Find the solution of the integral equation using Fourier transforms....