(a) Interpretation: The steady-state gain of the equation G ( s ) = Y ( s ) U ( s ) = 3e -s 10s+1 needs to be stated. Concept introduction: Steady-state gain is the steady-state value of transfer function which has been attended by a given unit step in the input.

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Answer 1

Question

Chapter 4, Problem 4.2E

Interpretation Introduction

(a)

Interpretation:

The steady-state gain of the equation G(s)=Y(s)U(s)=3e-s10s+1 needs to be stated.

Concept introduction:

Steady-state gain is the steady-state value of transfer function which has been attended by a given unit step in the input.

Interpretation Introduction

(b)

Interpretation:

The time constant needs to be determined.

Concept introduction:

The time constant usually is denoted by using the Greek letter τ, which is the parameter characterizing the response to a step input of a first-order, linear time-invariant system. The time constant is the main characteristic unit of a first-order system.

Interpretation Introduction

(c)

Interpretation:

The value of the output Y(t) needs to be determined when the value of t→∞ and U(s)=4s.

Concept introduction:

Steady-state gain is the steady-state value of transfer function which has attended by given unit step in the input.

Interpretation Introduction

(d)

Interpretation:

The value of output needs to be determined, when t=10 and the input is the same and also the output needs to be determined when expressed as the fraction of the new steady-state equation.

Concept introduction:

Steady-state gain is the steady-state value of transfer function which has attended by given unit step in the input.

Interpretation Introduction

(e)

Interpretation:

The value of the output needs to be determined.

Concept introduction:

A final value theorem requires the time domain actions to be determined simply by taking a maximum of a frequency domain expression, as opposed to translating by adding the limit to a time-domain expression.

Interpretation Introduction

(f)

Interpretation:

The output value of the given equation if u(t)=δ(t), t=0 and t→∞ needs to be determined.

Concept introduction:

Steady-state gain is the steady-state value of transfer function which has attended by given unit step in the input.

Interpretation Introduction

(g)

Interpretation:

The output value of the given equation needs to be determined, if u(t)=5 sin(2t), when t→∞.

Concept introduction:

Steady-state gain is the steady-state value of transfer function which has attended by given unit step in the input.

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Answer 2

Question

Chapter 4, Problem 4.2E

Interpretation Introduction

(a)

Interpretation:

The steady-state gain of the equation G(s)=Y(s)U(s)=3e-s10s+1 needs to be stated.

Concept introduction:

Steady-state gain is the steady-state value of transfer function which has been attended by a given unit step in the input.

Interpretation Introduction

(b)

Interpretation:

The time constant needs to be determined.

Concept introduction:

The time constant usually is denoted by using the Greek letter τ, which is the parameter characterizing the response to a step input of a first-order, linear time-invariant system. The time constant is the main characteristic unit of a first-order system.

Interpretation Introduction

(c)

Interpretation:

The value of the output Y(t) needs to be determined when the value of t→∞ and U(s)=4s.

Concept introduction:

Steady-state gain is the steady-state value of transfer function which has attended by given unit step in the input.

Interpretation Introduction

(d)

Interpretation:

The value of output needs to be determined, when t=10 and the input is the same and also the output needs to be determined when expressed as the fraction of the new steady-state equation.

Concept introduction:

Steady-state gain is the steady-state value of transfer function which has attended by given unit step in the input.

Interpretation Introduction

(e)

Interpretation:

The value of the output needs to be determined.

Concept introduction:

A final value theorem requires the time domain actions to be determined simply by taking a maximum of a frequency domain expression, as opposed to translating by adding the limit to a time-domain expression.

Interpretation Introduction

(f)

Interpretation:

The output value of the given equation if u(t)=δ(t), t=0 and t→∞ needs to be determined.

Concept introduction:

Steady-state gain is the steady-state value of transfer function which has attended by given unit step in the input.

Interpretation Introduction

(g)

Interpretation:

The output value of the given equation needs to be determined, if u(t)=5 sin(2t), when t→∞.

Concept introduction:

Steady-state gain is the steady-state value of transfer function which has attended by given unit step in the input.

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Answer 3

Question

Chapter 4, Problem 4.2E

Interpretation Introduction

(a)

Interpretation:

The steady-state gain of the equation G(s)=Y(s)U(s)=3e-s10s+1 needs to be stated.

Concept introduction:

Steady-state gain is the steady-state value of transfer function which has been attended by a given unit step in the input.

Interpretation Introduction

(b)

Interpretation:

The time constant needs to be determined.

Concept introduction:

The time constant usually is denoted by using the Greek letter τ, which is the parameter characterizing the response to a step input of a first-order, linear time-invariant system. The time constant is the main characteristic unit of a first-order system.

Interpretation Introduction

(c)

Interpretation:

The value of the output Y(t) needs to be determined when the value of t→∞ and U(s)=4s.

Concept introduction:

Steady-state gain is the steady-state value of transfer function which has attended by given unit step in the input.

Interpretation Introduction

(d)

Interpretation:

The value of output needs to be determined, when t=10 and the input is the same and also the output needs to be determined when expressed as the fraction of the new steady-state equation.

Concept introduction:

Steady-state gain is the steady-state value of transfer function which has attended by given unit step in the input.

Interpretation Introduction

(e)

Interpretation:

The value of the output needs to be determined.

Concept introduction:

A final value theorem requires the time domain actions to be determined simply by taking a maximum of a frequency domain expression, as opposed to translating by adding the limit to a time-domain expression.

Interpretation Introduction

(f)

Interpretation:

The output value of the given equation if u(t)=δ(t), t=0 and t→∞ needs to be determined.

Concept introduction:

Steady-state gain is the steady-state value of transfer function which has attended by given unit step in the input.

Interpretation Introduction

(g)

Interpretation:

The output value of the given equation needs to be determined, if u(t)=5 sin(2t), when t→∞.

Concept introduction:

Steady-state gain is the steady-state value of transfer function which has attended by given unit step in the input.

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Answer 4

Question

Chapter 4, Problem 4.2E

Interpretation Introduction

(a)

Interpretation:

The steady-state gain of the equation G(s)=Y(s)U(s)=3e-s10s+1 needs to be stated.

Concept introduction:

Steady-state gain is the steady-state value of transfer function which has been attended by a given unit step in the input.

Interpretation Introduction

(b)

Interpretation:

The time constant needs to be determined.

Concept introduction:

The time constant usually is denoted by using the Greek letter τ, which is the parameter characterizing the response to a step input of a first-order, linear time-invariant system. The time constant is the main characteristic unit of a first-order system.

Interpretation Introduction

(c)

Interpretation:

The value of the output Y(t) needs to be determined when the value of t→∞ and U(s)=4s.

Concept introduction:

Steady-state gain is the steady-state value of transfer function which has attended by given unit step in the input.

Interpretation Introduction

(d)

Interpretation:

The value of output needs to be determined, when t=10 and the input is the same and also the output needs to be determined when expressed as the fraction of the new steady-state equation.

Concept introduction:

Steady-state gain is the steady-state value of transfer function which has attended by given unit step in the input.

Interpretation Introduction

(e)

Interpretation:

The value of the output needs to be determined.

Concept introduction:

A final value theorem requires the time domain actions to be determined simply by taking a maximum of a frequency domain expression, as opposed to translating by adding the limit to a time-domain expression.

Interpretation Introduction

(f)

Interpretation:

The output value of the given equation if u(t)=δ(t), t=0 and t→∞ needs to be determined.

Concept introduction:

Steady-state gain is the steady-state value of transfer function which has attended by given unit step in the input.

Interpretation Introduction

(g)

Interpretation:

The output value of the given equation needs to be determined, if u(t)=5 sin(2t), when t→∞.

Concept introduction:

Steady-state gain is the steady-state value of transfer function which has attended by given unit step in the input.

Expert Solution & Answer

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Answer 5

Chapter 4, Problem 4.2E

Interpretation Introduction

(a)

Interpretation:

The steady-state gain of the equation G(s)=Y(s)U(s)=3e-s10s+1 needs to be stated.

Concept introduction:

Steady-state gain is the steady-state value of transfer function which has been attended by a given unit step in the input.

Interpretation Introduction

(b)

Interpretation:

The time constant needs to be determined.

Concept introduction:

The time constant usually is denoted by using the Greek letter τ, which is the parameter characterizing the response to a step input of a first-order, linear time-invariant system. The time constant is the main characteristic unit of a first-order system.

Interpretation Introduction

(c)

Interpretation:

The value of the output Y(t) needs to be determined when the value of t→∞ and U(s)=4s.

Concept introduction:

Steady-state gain is the steady-state value of transfer function which has attended by given unit step in the input.

Interpretation Introduction

(d)

Interpretation:

The value of output needs to be determined, when t=10 and the input is the same and also the output needs to be determined when expressed as the fraction of the new steady-state equation.

Concept introduction:

Steady-state gain is the steady-state value of transfer function which has attended by given unit step in the input.

Interpretation Introduction

(e)

Interpretation:

The value of the output needs to be determined.

Concept introduction:

A final value theorem requires the time domain actions to be determined simply by taking a maximum of a frequency domain expression, as opposed to translating by adding the limit to a time-domain expression.

Interpretation Introduction

(f)

Interpretation:

The output value of the given equation if u(t)=δ(t), t=0 and t→∞ needs to be determined.

Concept introduction:

Steady-state gain is the steady-state value of transfer function which has attended by given unit step in the input.

Interpretation Introduction

(g)

Interpretation:

The output value of the given equation needs to be determined, if u(t)=5 sin(2t), when t→∞.

Concept introduction:

Steady-state gain is the steady-state value of transfer function which has attended by given unit step in the input.

Answer 6

Chapter 4, Problem 4.2E

Interpretation Introduction

(a)

Interpretation:

The steady-state gain of the equation G(s)=Y(s)U(s)=3e-s10s+1 needs to be stated.

Concept introduction:

Steady-state gain is the steady-state value of transfer function which has been attended by a given unit step in the input.

Answer 7

Chapter 4, Problem 4.2E

Interpretation Introduction

(a)

Interpretation:

The steady-state gain of the equation G(s)=Y(s)U(s)=3e-s10s+1 needs to be stated.

Concept introduction:

Steady-state gain is the steady-state value of transfer function which has been attended by a given unit step in the input.

Answer 8

Interpretation Introduction

(b)

Interpretation:

The time constant needs to be determined.

Concept introduction:

The time constant usually is denoted by using the Greek letter τ, which is the parameter characterizing the response to a step input of a first-order, linear time-invariant system. The time constant is the main characteristic unit of a first-order system.

Answer 9

Interpretation Introduction

(b)

Interpretation:

The time constant needs to be determined.

Concept introduction:

The time constant usually is denoted by using the Greek letter τ, which is the parameter characterizing the response to a step input of a first-order, linear time-invariant system. The time constant is the main characteristic unit of a first-order system.

Answer 10

Interpretation Introduction

(c)

Interpretation:

The value of the output Y(t) needs to be determined when the value of t→∞ and U(s)=4s.

Concept introduction:

Steady-state gain is the steady-state value of transfer function which has attended by given unit step in the input.

Answer 11

Interpretation Introduction

(c)

Interpretation:

The value of the output Y(t) needs to be determined when the value of t→∞ and U(s)=4s.

Concept introduction:

Steady-state gain is the steady-state value of transfer function which has attended by given unit step in the input.

Answer 12

Interpretation Introduction

(d)

Interpretation:

The value of output needs to be determined, when t=10 and the input is the same and also the output needs to be determined when expressed as the fraction of the new steady-state equation.

Concept introduction:

Steady-state gain is the steady-state value of transfer function which has attended by given unit step in the input.

Answer 13

Interpretation Introduction

(d)

Interpretation:

The value of output needs to be determined, when t=10 and the input is the same and also the output needs to be determined when expressed as the fraction of the new steady-state equation.

Concept introduction:

Steady-state gain is the steady-state value of transfer function which has attended by given unit step in the input.

Answer 14

Interpretation Introduction

(e)

Interpretation:

The value of the output needs to be determined.

Concept introduction:

A final value theorem requires the time domain actions to be determined simply by taking a maximum of a frequency domain expression, as opposed to translating by adding the limit to a time-domain expression.

Answer 15

Interpretation Introduction

(e)

Interpretation:

The value of the output needs to be determined.

Concept introduction:

A final value theorem requires the time domain actions to be determined simply by taking a maximum of a frequency domain expression, as opposed to translating by adding the limit to a time-domain expression.

Answer 16

Interpretation Introduction

(f)

Interpretation:

The output value of the given equation if u(t)=δ(t), t=0 and t→∞ needs to be determined.

Concept introduction:

Steady-state gain is the steady-state value of transfer function which has attended by given unit step in the input.

Answer 17

Interpretation Introduction

(f)

Interpretation:

The output value of the given equation if u(t)=δ(t), t=0 and t→∞ needs to be determined.

Concept introduction:

Steady-state gain is the steady-state value of transfer function which has attended by given unit step in the input.

Answer 18

Interpretation Introduction

(g)

Interpretation:

The output value of the given equation needs to be determined, if u(t)=5 sin(2t), when t→∞.

Concept introduction:

Steady-state gain is the steady-state value of transfer function which has attended by given unit step in the input.

Answer 19

Interpretation Introduction

(g)

Interpretation:

The output value of the given equation needs to be determined, if u(t)=5 sin(2t), when t→∞.

Concept introduction:

Steady-state gain is the steady-state value of transfer function which has attended by given unit step in the input.

Answer 20

Expert Solution & Answer

Answer 21

Expert Solution & Answer

Answer 22

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Answer 23

Ch. 4 - Prob. 4.1E Ch. 4 - Prob. 4.2E Ch. 4 - Prob. 4.3E Ch. 4 - Prob. 4.4E Ch. 4 - Prob. 4.5E Ch. 4 - A stirred-tank blending system can be described by...Ch. 4 - Prob. 4.7E Ch. 4 - Prob. 4.8E Ch. 4 - Prob. 4.9E Ch. 4 - Prob. 4.10E

(a) Interpretation: The steady-state gain of the equation G ( s ) = Y ( s ) U ( s ) = 3e -s 10s+1 needs to be stated. Concept introduction: Steady-state gain is the steady-state value of transfer function which has been attended by a given unit step in the input.

Solution Summary: The author explains the steady-state gain of the equation 3.

(a)

Interpretation:

The steady-state gain of the equation G(s)=Y(s)U(s)=3e-s10s+1 needs to be stated.

Concept introduction:

Steady-state gain is the steady-state value of transfer function which has been attended by a given unit step in the input.

(c)

Interpretation:

The value of the output Y(t) needs to be determined when the value of t→∞ and U(s)=4s.

Concept introduction:

Steady-state gain is the steady-state value of transfer function which has attended by given unit step in the input.

(f)

Interpretation:

The output value of the given equation if u(t)=δ(t), t=0 and t→∞ needs to be determined.

Concept introduction:

Steady-state gain is the steady-state value of transfer function which has attended by given unit step in the input.

(g)

Interpretation:

The output value of the given equation needs to be determined, if u(t)=5 sin(2t), when t→∞.

Concept introduction:

Steady-state gain is the steady-state value of transfer function which has attended by given unit step in the input.

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Chapter 4 Solutions

(a) Interpretation: The steady-state gain of the equation G ( s ) = Y ( s ) U ( s ) = 3e -s 10s+1 needs to be stated. Concept introduction: Steady-state gain is the steady-state value of transfer function which has been attended by a given unit step in the input.

Solution Summary: The author explains the steady-state gain of the equation 3.

(a) Interpretation: The steady-state gain of the equation G(s)=Y(s)U(s)=3e-s10s+1 needs to be stated. Concept introduction: Steady-state gain is the steady-state value of transfer function which has been attended by a given unit step in the input.

(c) Interpretation: The value of the output Y(t) needs to be determined when the value of t→∞ and U(s)=4s. Concept introduction: Steady-state gain is the steady-state value of transfer function which has attended by given unit step in the input.

(e) Interpretation: The value of the output needs to be determined. Concept introduction: A final value theorem requires the time domain actions to be determined simply by taking a maximum of a frequency domain expression, as opposed to translating by adding the limit to a time-domain expression.

(f) Interpretation: The output value of the given equation if u(t)=δ(t), t=0 and t→∞ needs to be determined. Concept introduction: Steady-state gain is the steady-state value of transfer function which has attended by given unit step in the input.

(g) Interpretation: The output value of the given equation needs to be determined, if u(t)=5 sin(2t), when t→∞. Concept introduction: Steady-state gain is the steady-state value of transfer function which has attended by given unit step in the input.

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Chapter 4 Solutions

(a)

Interpretation:

The steady-state gain of the equation G(s)=Y(s)U(s)=3e-s10s+1 needs to be stated.

Concept introduction:

Steady-state gain is the steady-state value of transfer function which has been attended by a given unit step in the input.

(c)

Interpretation:

The value of the output Y(t) needs to be determined when the value of t→∞ and U(s)=4s.

Concept introduction:

Steady-state gain is the steady-state value of transfer function which has attended by given unit step in the input.

(f)

Interpretation:

The output value of the given equation if u(t)=δ(t), t=0 and t→∞ needs to be determined.

Concept introduction:

Steady-state gain is the steady-state value of transfer function which has attended by given unit step in the input.

(g)

Interpretation:

The output value of the given equation needs to be determined, if u(t)=5 sin(2t), when t→∞.

Concept introduction:

Steady-state gain is the steady-state value of transfer function which has attended by given unit step in the input.