Find the inverse z transforms of the following two transfer functions: z+0.6 H1 (z) = (z² + 0.8z + 0.5)(z – 0.4) (I + 2)(t'0+ 2) H2(z) = z(5'0 – 2)

Q: 2²u at² ·x 20u = 0, əx² -∞0 0 the equation subject to the initial and boundary conditions: u(x,0) =…

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Q: i). ƒ (1) = (5– 312) ² i). ƒ (1) =r2sinh (21) Find the Laplace transforms of the following…

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Q: 2y" – 2y' + 2y = -cos(3t), y(0) = 0, y'(0) = 1 6.

A: Given differential equation is 2y''-2y'+2y=-cos(3t)                  (1) y(0)=0, y'(0)=1 Let the…

Q: Use matrix to solve for X(s) and Y(s) in the equations below and find the laplace transform of X(s)…

A: To solve the given problem Simplify for X(s) and Y(s)  Using inverse laplace transformation solve…

Q: Use laplace transformation to solve the following differential euqations. Show all the steps…

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Q: cos x, 0 a

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Q: E. Problem Solving Using Laplace transforms, find the solution to the following system of equations…

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Q: f'(t) = f"(t), ƒ(0) = 2, f'(0) = 0, f"(0) =

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Q: plve the following DE using a suitable type of transformation. ý = x + y (let v = x + y)

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Q: cos x, 0a

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Q: Solving y' + 4y = 8(t) with y(0) = 0 %3D using Laplace transforms with a convolution necessitates…

A: The given differential equation is y'+4y=δ(t) Taking Laplace transform on both sides we get…

Q: Find the Fourier transforms of the following functions: a). f(x) = # 0 x < 0 e−x x ≥ 0

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Q: Given 30<t ₹2 10 elsewhere find Fw), the Fourier transform of ƒ(t). Compute the values of F(0), F(1)…

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Q: the first question: Find the volume V of the solid obtained by rotating the region bounded by the…

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Q: Solve the given initial value problem using the method of Laplace transforms. Sketch the graph of…

A: (.)  Given differential equation is,         w''+w = 2u(t-3)-u(t-4) ;   w(0) = 2  ,  w'(0)=0 (.)…

Q: Use the Divergence Theorem to calculate the surface integral || F. dS; that is, calculate the flux…

A: According to divergence theorem ∫∫SF.ds=∬∫VdivF dxdydz Given Fx,y,z=cosz+xy2i+xe-zj+siny+x2zk…

Q: y""-4y" +5y'-2y = 7t-5, y(0) = 0, y'(0) = 0, y"(0) = -2

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Q: 3. a) Find the Fourier transform of g(x) given that g(x) = 3e¬4|x+2| b) Using the formulas for…

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Q: Find the Laplace transform of the following: 2y+3y"-23y - 12y = 5t-7, y(0) = 0, y'(0) = 0, y" (0) =…

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Q: Solve the given initial value problem using the method of Laplace transforms. y'' + 7y' +…

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Q: Use the Laplace transformation to solve the following ODE: y''-y'-12y=2e2t, with y(0)=7, y'(0)=0.…

A: Given: The given ordinary differential equation is y''-y'-12y=2e2t with y(0)=7 ,y'0=0

Q: dt? + w?) G(t) = 6(t) () 1. Now using the Fourier transformation on both sides of equation 1 and…

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Q: Find the Fourier transform of f(t) = {, t 0 12e-t O 2/(1+jw) O 1/(1+jw) O -1(1+jw) O -2/(1+jw)

A: We have to find the Fourier transform.

Q: 2+5( jw) (jw)' +3( jw)–10 a- F(w)=-

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Q: F (ƒ') - {¹(- Ji(- (-5w+4w2), (a) Find an expression for f (w) in terms of unit step functions u w…

A: Let us start solving the problem step by step  We must find the values of f(w) F(x) and g(x)

Q: d³y d²y 3 dx3 3 – y = x²e*; y(0) = 1, y'(0) = 2, y"(0) = 3 dy dx2 dx

A:

Q: Use the InverseFourierTransform function of Mathematica or Wolfram Alpha to find the (spatial)…

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Q: Determine the Laplace transform of the function. a) [4+sin(31)+5e²]- b) Z[6r'+2t’e" +sinh(4)].

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Q: Use laplace transformation to solve the following differential euqations. Show all the steps…

A: Some of the properties of Laplace transformation…

Q: y''-10y'+9y=5t,  y(0)=-1        y'(0)=2

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Q: ®[6.4] Using the Laplace transform to solve IVP. yu t16y= 43(t-37) H10)=2 , y'0) =0 y10)%=D2 %3D 3D0

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Q: 8z + 22 – 23 3. Find the causal inverse z-transform of X(2) = %3D (z – 1)(z – 3)²

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Q: [SK 23. Find the cosine transform of the function off(x), if f(x) = { CoS x, ) a

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Q: Determine the Fourier transform of the function f(t) = H (t)e-5t

A: Heaviside unit step function, H(t)=0,t&lt;01,t&gt;0By the definition of Fourier transformation,…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.