(CONTROL SYSTEM) 1: Direction: solve for y(t) if all initial conditions are zero. Use Laplace transforms a) dy3 dt 3 + ²-15-12y = 5u(t). dt

Q: Y = f+₁ + fot-, h= 71

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Q: Q2: if it was Ø(x,y, z) = 3x²y – y°z³ Find the regression of this function at the point (1,-2,-1)

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Q: Express the equation in Heaviside Function

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Q: d 3x 3 ) y = = e dx

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Q: Let Dx be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

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Q: Find the Laplace transform of: 1. f(t) = e(-3t) sin(2t) cos(3t) cosh(t)

A: Given that 1) f(t) = e-3tsin (2t) cos (3t) cosh (t) 2) f(t) = 1+sin t + (8t)15 + t2cos 3t We have to…

Q: inverse laplace

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Q: 6 (2) Find and draw the Fourier transform of f(t) = 9+t²

A: Find and draw the Fourier transform of f(t)= 6/(9+t^2)

Q: Use the definition to find the Laplace Transform of the given function (t, 0st<1 f(t)= OSt<1 1, t21

A: The Laplace transform of the function f(t) is represented as F(s) or L[f(t)], it is defined as…

Q: A 4-pound weight stretches a spring 2 feet. The weight is released from rest 12 inches above the…

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Q: 5s F(s) %3D (s + 7) (s? + 4) 35 35 10 -7t Answer: f(t) G, cos2t + sin2t) 53 %3D 53 33

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Q: * + 5x + 6x = 5sin (2t)

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Q: Apply Fourier transform, jw F(w) = F₁ (w) + F₂ (w)...... equation 2 |F₁(t) = −8(t + 2) +…

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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: 3s Find the Inverse Laplace of s2+4

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Q: Find the local linearization of f(I) = 1/1 at-3. %3D Ls(z) =U %3D

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Q: Show that the function f(x; y; z) = 2z3- 3(x2+y2)z  satisfies the Laplace equation.

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Q: aw Use the functions below to (a) express as a function of t, both by using the Chain Rule and by…

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Q: Determine the constants a, p, yo and y'o so that 3S +3 Y(s) = (s + 2)² is the Laplace transform of…

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Q: dx Graph the slope field for the equation dt -r(x² - 4) and attach it to the solution. Draw (by hand…

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Q: Using transform ,find the result of the integral x =rcos(0), y =rsin(0) e-(7x2+3y") dxdy

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Q: Laplace transform

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Q: %3D b)ë + 4x = t,x(0) = 1,x(0) = 0 %3D

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Q: dy dx (²), y(a)= A. (a) Show that by introducing the new dependent variable v(x) by the relation y =…

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Q: y′ = t2 + y2

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Q: Find the inverse Laplace transforms. (A) F(s) = (B) F(s) = 5s +1 s² - 25 1 (s+a)(s+b)

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Q: 4.1 Solve by Laplace Transformation U+ + Ux₁ = xt with I.C: u(x₂0) = Sinx ; u(ost) = 0

A: 4. To solve the given partial differential equation (PDE) using Laplace transform, we will follow…

Q: Determine the integrating factor of z = 2xy – x %3D -2x 2e 2 2x e Option 3 O Option 1 None of the…

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Q: Find the Saution of the equation using Inver's operator method y + 3y + 2Y = 4 cos(x)

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