1. Obtain Pole, zero, gain values of the transfer functions given below. Also verify your result theoretically 1 A. G(s) = s2+s+4 B. G(s) %3D s2+9 1 C. G(s) (s2+3s+5)(s+3)(s+5)

Q: Derive the transfer function H(s)/Q(s) for the liquid level system shown in Fig. below. When (a) The…

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Q: c) The transfer function of a system is Y (s) 10(s +1)(s+2) R(s) (s+3)(s² +6s+25) Determine y(t)…

A: please see the next step for solution

Q: 4) Compute and sketch the output y(t) of the continuous-time LTI system with impulse response h(t) =…

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Q: 4 3. Apply Euler-Maruyama method as one step to solve the SDE dy = 3/dt+dB₁ 5-1 y(1) = 2

A: Given that the SDE is dy=3-y5-tdt+dBty1=2

Q: 25 Given the transfer function G (s) the values of Ċ and wn are : s2+10s+25 (=1 and wn=5 (=0 and…

A: G(s)=25s2+10s+25we know that  ω2n=25⇒ωn=52ζωn=102ζ×5=10ζ=1

Q: Solve the initial value problem with x'(t) = A, for t20 with x(0)= Classify the nature of the origin…

A: Given matrix is A=-1-39-13 We find eigenvalues.…

Q: Suppose a population of P(t) satisfies dp/dt = 0.4P -0.001P 2 P(0) = 50 A. What is the carrying…

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Q: Find the elgenpairs of matrix A and the vector Kty such that the initial vahue problem * = Ax, x(0)…

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Q: Suppose a population of P(t) satisfies dP dt 0.4P - 0.001P² P(0) = 50 a What is the carrying…

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Q: 1. Use the Chain Rule to find dy in term dr а у — (и— 2)3 and и - 2x + 1 b. y = Jū and u=5x² – 3 1 1…

A: In this question we will use basic of calculus i.e differentiation by using chain rule. We will…

Q: Soru 1 Solve the given initial value problem using the method of Loplace transforms. y "+6 y'+ 5y=12…

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Q: 7 Find the second linearly solution of the D.E x'y"+xy'-(x+2)y = 0, given that: y,(x) =

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Q: If the roots of characteristic equation of a given transfer function are 3-j5,3+j5 and -4, then the…

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Q: b. For the given root locus graph figure 2 determine the following i. The open loop transfer…

A: Part(1): From the given diagram we have, The open-loop transfer function is, kss+8s+12 So, the poles…

Q: Determine the steady-state gain of a system having transfer function 20(1+3s) G(s) = + 7s + 10

A: Given transfer function is Gs=201+3ss2+7s+10 W have to determine the steady-state gain of the…

Q: Verify the final value theorem of f(t) = e¯t(t + 2)². 2 0 4 6 = Find the initial value of the…

A: Given  f(t)=e-t(t+2)2 X(s)=808s(s2+2s+101)

Q: 3) The closed loop transfer function for a second order system is: T(s) 4/ (s? + 4 + 4). Calculate…

A: The standard transfer is: y(s)x(s)=kωn2s2+2ωnδs+ωn2 The given equation  T(s)=4(s2+4s+4) Comparing…

Q: Given the open- loop transfer function below: KG(s)H(s)=(K(s-A)(s-B))/((s+C)(s+D)) where A=1, B=5,…

A: For the given values of A, B, C, D, The open loop transfer function becomes KGsHs=Ks-As-Bs+Cs+D…

Q: 3-8 Use the Chain Rule to find dz/dt or dw/dt. 3. z = xy – x'y, x=t + 1, y =t - 1

A: 3) Given:        z=xy3-x2y where x=t2+1 and y=t2-1 substituting x and y values in z…

Q: In parabolic PDES, to apply the difference method to find the solution of a function T(x,t), we…

A: We have the parabolic partial differential equation system represented by the following diagram, We…

Q: find the critical points for dA=2A=0.01 AL and dL/dt=-0.5L+0.0001AL

A: Critical points are the points in a graph, at which the direction of graph changes.

Q: 11: Given the function f(X) = 8x2 - 4x₁x₂ + 5x and Xo = [5 2]. Then G-¹g at Xo is equal (( G is the…

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Q: The system in Section 3.2 - Exercise 3 (previous page): dy dr 5x + 4y dt 9x dt

A: Since you have posted multiple questions and we can answer one question. So, answered the first…

Q: In the study of a nonlinear spring with periodic forcing, the equation y"+ ky + ry -A cos ot arises.…

A: The equation of non linear spring is y''+ky+ry3=Acosωt. The value of k is 5, A is 7, r is 2 and ω is…

Q: A system is represented by the transfer function Y(s) 10.4 s² + 47s + 160 = R(s) s³ + 14s² + 56s +…

A: We need to determine the state variable representation of the transfer function:…

Q: In 2019, A field in California has been completely devastated by fire. Two types of vegetation,…

A: “Since you have asked multiple questions, we will solve the first question for you only for the 1st…

Q: (b) Find the Wronskian W[y1,Y2](t) of y1 and y2-

A: W[y1,y2]= -t2et

Q: 2. Determine the expressions for the unit step response for the systems represented by the following…

A: 2) ii  Given,X0sxis=10s2+65+5Given , unit step responsexis=1/sX0s =10ss2+65+5X0s =10ss+1s+5using…

Q: s2+2 s+1 S s+1 52–2s (4) s(s²+4) s+2s (2) s2+2 (3) s2+2 (5) (1) input=x(t) output=y(t) diferantial…

A: Find the explanation below

Q: s+6 1 For the system with forward path gain G(s) and feedback gain H(s) = 814 input R(s) = ° will…

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Q: Consider the linear ODE *'y() + 6a?y" + 4®y/ – 4y = 0 (a) Verify that y1 = *, 2 = -2 and y3 = -2 In…

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Q: Consider the system: dx/dt=4x(1-2x)-xy dy/dt=2y-4xy (a) Are these species predator-prey or…

A: Consider the given system of equations.

Q: For the characteristic equation s4 + 67s13+ 13512-8- 20s7 + 425 +: 5+s+25 + 252 + 7s + 15 = 0 of a…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: For the system dx 2 x-( ² ) x + (56). 5 0-5 dt 40 determine the critical point x = xº, and then…

A: For the system: dxdt=520-5x+-5640, we need to determine the critical point and then classify it.

Q: The open-loop transfer function for a system is K(s + 1) G(s)H(s) %3D s(s - 1)(s² + 4s + 16) Use…

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Q: Q1: The relation between the input u(t) and the out put y(t) of the system is given as : dy(t) /dr +…

A: To find transfer function , take Laplace Transform on both side of differential equation and put…

Q: Put the following initial value problem into a first order system form. (Show your workl) y(0) – 3y"…

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Q: For the system dx 1 -23 x+ dt -5 15 determine the critical point x = x', and then classify its type…

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Q: -2x y' = y - x y'e* diferansiyel denkleminin genel çözümünü bulunuz.

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Q: 3s+6s+1 QI)Realise the Transfer Function Z21 with a lattice network. 2(s+1)(s+2)(s+3)

A: Given Z21=3s2+6s+12s+1s+2s+3

Q: 4.9- Sketch Bode plots for the following transfer function: s2 (s + 1)(s² + 4s + 16)

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Q: D1.22 For the following systems with outputs y and inputs r, find the transfer functions: (a) drz…

A: Given (a) d2ydt2+3dydt+7y=6r1+5r2-4dr2dt2 (b) d2y1dt2+6dy1dt+2y1=drdt-3rdy2dt+6y2=4drdt (c)…

Q: • Obtain the transfer function T(s) from following state space representation. 1 10 1x+ и -1 -2 -3 y…

A: Given state space representation  X˙=010001-1-2-3x+1000uY=100x+0·u Comparing with , X˙=Ax+BuY=Cx+Du…

Q: The transfer function of an control system has step response of 1-e-10t is a) 10/s(s+10) b) 10/s c)…

A: We have to solve given problem:

Q: the relationship between aphids, A, ( prey) and ladybugs, L, (preditor) can be described as follows:…

A: the critical point is find by comparing the derivative to zero.

Q: Suppose that the transfer function of this system is given by P(s) :

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Q: Example 2:Obtain the poles and zeros of the transfer function given below: s2 + 4s + 3 G(s) = %3D s3…

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Q: Calculate the poles and zeros of the systems with the following transfer functions. Comment on the…

A: Hello. Since your question has multiple parts(iv in both the problem), we will solve first question…

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.