5) Assume you have a plant defined by the transfer function G(s) %3D s+a Let Y(s) = G(s)U(s) where U(s) is an input to the plant and Y(s) is the output. a) What is y(t) if U(s) is a cosine input i.e. U(s) ? Here, y(t) is the inverse s²+w² Laplace transform of Y(s). [Hint: Use PFE method]

5) Assume you have a plant defined by the transfer function G(s) %3D s+a Let Y(s) = G(s)U(s) where U(s) is an input to the plant and Y(s) is the output. a) What is y(t) if U(s) is a cosine input i.e. U(s) ? Here, y(t) is the inverse s²+w² Laplace transform of Y(s). [Hint: Use PFE method]

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: If a and b are integers, then a/b is always a rational number. True False

Q: Question 4 Find the gradient of the function at the given point. w = 2x - 4yz+z², (1, 1, −2) 21+…

Q: (E) 18. Consider the function f = e2"y – xy tan 3x+7. Compute the gradient of f, and compute all…

Q: Find the directional derivative of the function at P in the direction of v f(x,y,z xy + yz + xz,…

A: As per our guidelines we only solve one question and rest of the question will be reposted.

Q: If (x, y) moves from (-2, –1) towards (1, 5) for a distance 0.02, then which of the following is…

A: fx,y=exyPoints from−2,−1 towards 1,5 for a distance 0.02

Q: dw 1. Express both du as functions of u and v in two ways: (a) Using the Chain rule, and (b) First…

A: 14a) (a)Given w=x2y+xy2,x=u+v,y=u-v Use chain rule for the partial derivatives:…

Q: Suppose z = x² sin y, x = s² + 3t², y = 6st. Əz Əz A. Use the chain rule to find oz and 0 as…

A: Suppose .(A) By using chain rule to find as functions of .(B) To find the numerical values of when…

Q: Question: Find Y As A Function Of T If 16y" - 40y' + 25y = 0. Y(0) = 9, Y')O) = 5. Y = . Find y as a…

Q: Q2: Discuss the fundamental theorem for gradients using E = 5x2 i + 20 xy j+ 10 yz3 k and the…

A: Fundamental theorem of gradient states that a if line integral through a F gradient field depends…

Q: (c) Vf(x, y, z) = (2xy, x² – 2yz, 4 - y²) -

Q: Minimizing the length of the residual vector r = b – Ax is equivalent of mini- mizing the quadratic…

Q: onsider the following equation system: (P =r – Q – I+w P= α + Q | I = BQ + Vw here Q,P,I are the…

Q: yes, hi. I've seen another source, use set variables to 0 and then solve individually, answers are…

A: setting z=0 and solving for x and y. similarly setting y=0 and solving for x and z.

Q: = 0. c) y(0) = 1, y'(0) = 0, y"(0) = -1. Is the set of functions linearly independent or linearly…

Q: Make an example of an autonomous ODE, with stable equilibrium at -1 and 3, and an unstable…

Q: f (x, y) ~ bo + b1,0(x − 1)+b0,1(y−2)+ b2,0 (x - 1)² + b₁,1(x − 1)(y-2) + bo,2(y − 2)² +…...

A: We find the Taylor series of the given function

Q: B3. (a) Let y be a function of x, defined implicitly by the equation x?y + y3 + x = 0. Find the…

Q: Q2// B :- If u+v3e"cos y and u- v=e' sin y find the Jacobain of the function alu,v at dx.yl (x.y)…

Q: 4) Demand for a model of SUV is given by the formula: √x D(x, y) = 45,000 10 (5y - 11)3/2 where x is…

A: Demand for a model of SUV is given by the formula, D(x,y)=45000-x2-10(5y-11)32 We have to find the…

Q: (a) Find the directional derivative of f(r, y, z) = 8ry2-+y at the point (1,1, 1) in the direction…

Q: 1 Find the partial derivative with respect to y of the function (2 x – 3) (3 y + 1)i el-5 z+5). -5…

A: To find the partial derivative of the given function with respect to y (2x-3)1/4(3y+1)1/4e(-5z+5)

Q: alu,v at dx,yl Q2// B :- If u+v=e"cos y and u- v=e" sin y find the Jacobain of the function (х,у)…

Q: For the generating function A(z)=- find the corresponding r≥ 0. 1-9z

A: Given: The function generating function is Az=21-9z2. To find: The numeric function corresponds to…

Q: Find the gradient of the function f(x,y) = 10y - 2x at the point (2,9). Then sketch the gradient and…

Q: - 4( Let u(t) = 8t i+ (-9)j-8k and v(t)= e'i+9 ej- e "k. Compute the derivative of the following…

A: topic - dot product and derivative of a function

Q: 12. Findofy-7 a Find the gradient of the greph atos b) Show that the above graph has turning points…

A: Given-(a)-Equation y=x3-3x2+7...(1)Differentiate abive equation with respect to x we get that…

Q: Find the gradient of the function at the given point. w = 5x²y-7yz+z², (1, 1, -2) O 15i+ 26j+ 11k O…

Q: 4. xyzx + 2y³ (2)³ = 1 Dependent variable/s: Independent variable/s: Type: Order: Degree: Linearity:

A: Solution : To discuss about the nature of given differential equations

Q: dz (е) dz

Q: Consider the following graph. Let u-(t) = u(t – 7) be the unit step function shifted 7 units to the…

Q: Example: Sketch the direction field for equation: y' = y(2 – y). (1) Evaluate slopes at several y's.…

A: Slopes of y's yy'=y(2-y)y=3-3y=20y=11y=00

Question

5)
Assume you have a plant defined by the transfer function G(s) =
1
%3D
s+a
Let Y(s) = G(s)U(s) where U(s) is an input to the plant and Y(s) is the output.
a) What is y(t) if U(s) is a cosine input i.e. U(s) =
? Here, y(t) is the inverse
s²+w²
Laplace transform of Y(s). [Hint: Use PFE method]
b) What is y(t) if U(s) is a step input ?

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Chain Rule$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

6
Activity 3: Find the derivative, dy/dx of the following using the chain rule: a) y = . 'x+1 b) у %3 5x+1° c) y = ()5. 'x+1° 3 d) у 3 Зх+1 e) y = xVx2 + 2 f) y = xvx2 – t) у%3D хVх2 — 2 - g) y = xV3 – x² h) y = xV4 +x²
Which of the following functions V(y1, y2) is a Lyapunov function for the dynamical system y₁ = (4-₁)ex, y2 = y²-y²y₂ Select one: a. V(v₁.32) = -4+(2-1)³ b. V(v₁.y2) = -²³ +²² c. V(v₁.92) = ₁ + y/² C. Od. V(y₁, y2) = (y₁ - 4)4+ (y2 - 1)²
a) For Z1 = -4 + 3j and Z2 = 3 -- j. Find: %3D (i)Z, + Z2 Z2 (ii) z Note: Each solution should be represented in both rectangular and polar form b) Given 3 + jA = (r + jy)(1 + j) Find æ and y, wliere a and y are real nunbers and show your answer is correct. c) Find: (15 + 8j)
Calculate the first derivative of a general cubic Bezier curve .We have a Bezier curve C1, that is described from the control points P0(0,0) , P1(3,3,),P2(6,3), and P3(8,1), and curve C2 that is described from the control point P4,P5,P6(11,5) and P7(15,9). Draw the curve C1 approximately and a control polygon
Theorem". The bisection approach is always Convergent proof we have | α-{\
consider the function f(x, y) esin(@) y Write the gradient vector Vf A vf = esin(#) (sin(x), 1) RVf = esin(=) (cos(x), 1) C Vf = esin(=) (cos(x)y, 1) Vf = esin(æ) (y, 1) D
Question 6. Consider the function f: R2 R determined by f(x)=x | 12 24 2 3 +2. -> (a) Find the gradient and Hessian of f at the point (1, 1). (b) Find the directional derivative of f at (1, 1) in the direction of the maximal rate of increase. (c) Find a point that satisfies the first order necessary condition. Does the point also satisfy the second order necessary condition for a minimum? [15 marks]