Transform: F (s) 18-16 s²-08-13 Of(t) = 4e 3 sin2t – 4e-3t 31 cos2t O f(t) = 4e³t cos2t 4c sin2t O f(t) = 4e 3¹ cos2t 4e-3 sin2t O f(t) = 4e³ sin2t4e³ cos2t

Q: In the case where a = -T and b = T, compute (sin px, sin qx), (sin px, cos qx), and (cos px, cos…

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Q: 5 sin [ -5TT X<ST %3D otherwise

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Q: 3i +2V2 - 5n -4i +6(1 +a T/4 [(3sec2 t)i - (5 + sin t)j - (6sec t tan t)k)]dt Find 0. 2 2-57T-4 3i +…

A: ∫sex2xdx =tanx+c∫(constant)dx=x+c∫sint dt =-cost +c∫sect tant dt =sect+c tanπ4=1cosπ4=12secπ4=2

Q: 2) f(t) = 4t3 sin %3D

A: we have to find Laplace transform

Q: 1] Evaluate (a) -S (s²+1) ² {t sin (b) S 1/2 5² (s² +¹)² (d) S

A: Find Laplace of tsin(t/2)

Q: Q6) -bt (a) Derive Fourier transform of the following signal: x(t) = 2ce za u(t). Then plot the…

A: Given: xt=2ce-bt2au(t)

Q: c) Use a pair (table) to findz-transform of x(n) = 20.65 √2 cos((-)n-1.415)u(n)

A: Introduction: There are many properties that are followed by Z-transformation. It helps us to…

Q: Find Laplace transform of the function f(t) = cos(2t + 3)+e¬'u(t – 4) + tcosh²2t

A: Use the following formulas while calculating the Laplace transform of the given function.…

Q: Let u(x,y)=4x+3x2y−y3. Part (a) Show that u is a harmonic function. Part (b) Find a harmonic…

A: The given problem is to show that the given function u(x,y) is harmonic function and also to find…

Q: O [-5, -1) U (1,6] O (-5,6] O [-5, 6] O (-5, -1] U [1, 6] Find the domain of r(t) = (ln(t + 5),…

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Q: evaluate

A: Given integral is evaluated as follows.

Q: cos° (nt)dt

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Q: Question 3 Find the Laplace Transform of e 2t cos3t + 5e 2t sin3t 15 + A s2+9 s2+9 s+17 B (s+2)²+9…

A: laplace transform

Q: Find Laplace f(t) = t sin 2t + S transform of the function TU 2 cos 2t T 2

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Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

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Q: (e²t) LE9+² +6t+73 L{ 5 cos (4+) } -4t L {ett sin (8t) 3

A: Given that the Laplace functions Le2tL9t2+6t+7L5cos4tLe-4tsin8t .

Q: cos (3z) + sin(3z) c: |2| = 2 to be -dz: Calculate the integral value. 23 (Complex functions theory)

A: Answer

Q: x+yi dz (az + b)" if a = 4, b = 6, c = 10502, n = 3, x = 1, and y = 6. Then, find the imaginary…

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Q: laplace transform

A: Given function is yt=3e-tcost-2cos2t-sin2t We need to find the Laplace Transform of the function.

Q: Solve for the Laplace transform of sint sin 2t cos t

A: The given function is f(t)=sin t sin2t cost  rewrite the function as  f(t)=122sin t cost sin2t…

Q: (0.52)* ) 1 1+x²

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Q: What is the smallest number that can be represented as the sum of four positive squares (not…

A: Consider the given statement. Since we need to find a number, which is the smallest number of sum of…

Q: Find the Inverse Laplace Transform. F (s) = 6s-54 82 +16

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Q: Compute cos æ dæ. cos x +C 3 cos a sin x +C sin r cos a + cos x +C sin a +C 3 sin r + sin I 3 sin a…

A: Given, ∫cos3x dx We can write it as by using the trigonometric identity as, cos2x=1-sin2x∫cos3x…

Q: Find the Fourier transform specified in part (a) and then use it to answer part (b). (a) Find the…

A: In part (a) we have to find the Fourier transformation, Given, f(γ,p,t)=e-γtsin pt  t&gt;0,0…

Q: Calculate the complex exponential Fourier coefficients for the signal shown below Note:- the…

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Q: Solve the Laplace transform of: 3 cos 8t + 2 sin 8t

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Q: 2x³y' = y(2x² - y²)

A: We have to solve the given ordinary differential equation.

Q: If x(t) = 0.886 +3 cos (5wot) -sin(6wot) , then an , bn a0 5,-1, -6 O 0.886,-1,-6 O 5, -1,6 O…

A: To find the correct option

Q: Solve 8(t – nt)cos(-) dt

A: Given integral is ∫-∞∞δt-πtcos1Tdt