Laplace Transform Consider an LTI system described by: d²y(t) dy(t) dt² + 5y(t) = dr(t) dt dt (a) Determine the algebraic expression of the transfer function of the system (H(s)). + 3x(t).

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Q: How to find the characteristi dx(t)/dt=Ax(t)+Bu(t)

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A: We have to find the transfer function H(s) using given differential equation.

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Q: For the system dx It is Choose one dt = · ( õ ) x + (¯ 5 2 0 -5 -35 25 determine the critical point…

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Q: Let T: R² R2 be given by →> Find the matrix M of the inverse linear transformation, T-¹. M = -5 T(x)…

A: Suppose T:R2→R2 is given by T(x)=-1-5-34X      (1) To find the matrix M of the inverse linear…

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Q: (1 point) The matrices - [8]. [J]. -[i]·.^ - [i]· A A4 = A₁ = A3 = A₂ = form a basis for the linear…

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Q: 5) Find dx/dt of Matrix: X 5e-1 2e-¹ -7e-t

A: We know , d/dx(e-t) = -e-t   Given X = 5e-t2e-t-7e-t

Q: Exercise 5. (Fishery Model) The equation N = rN(1 –) – H represent a simple population model of a…

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Q: 11//(S²+S+1) Find the transfer function, G(s) = VR(S)/Vi(s)

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Q: dy 4. -+x-y dt 2r+212

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Q: Let f be the linear transformation represented by the matrix 2 -2 A = (2) 3 -2 Find the point (x, y)…

A: Given, A=2-23-2 Need to find the point x,y such that fx,y=-4,-1.

Q: linear transformation A maps P(1,0) to P’(-2,-4) and Q(0,1) to Q’(4,1). Find (i) The matrix A (ii)…

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Q: Consider the differential equation y" +9 y = 6 (t) + 5 (t – 2) for a system that is initially…

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Q: Let 0<θ<2π, θ ≠ π. Consider the linear transformation T: C^2→C^2 given by matrix [ cosθ -sinθ]…

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Q: (2) Consider the following vector ODE 2 1 1 Y': × - (D) - - () 0 2 -1 Y + 0 0 0 -1 (a) Convert it…

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Q: If v = (v1, v2) and T(v)=v except T(0, v2) = (0, 0) then T(v + u) = T(v) + T(u) showing that the…

A: Linear with respect to addition is given. We have to prove for scalar multiplication.

Q: Find the image of the line 2y = x under the transformation with matrix operator

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Q: 1. By using shortest path method, A. Consider the shortest route from node 1 to node 6, what is the…

A: Given: The given network is

Q: 5e- 2e- |-7e-/ X = Find dX/dt of Matrix:

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