Process Dynamics and Control, 4e
Process Dynamics and Control, 4e
4th Edition
ISBN: 9781119285915
Author: Seborg
Publisher: WILEY
Question
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Chapter 3, Problem 3.9E
Interpretation Introduction

(a)

Interpretation:

The functions of time that will appear in y(t) for the given function Y(s)=2s(s2+4s) is to be determined. Also, whether the function y(t) is oscillatory or has constant value for large values of t is to be determined.

Concept introduction:

For a function f(t), the Laplace transform is given by,

F(s)=L[f(t)]=0f(f)estdt

Here, F(s) represents the Laplace transform, s is a variable which is complex and independent, f(t) is any function of time which is being transformed, and L is the operator which is defined by an integral.

f(t) is calculated by taking inverse Laplace transform of the function F(s).

PFE is the partial fraction expansion is the method of expanding the denominator of a fraction into simpler terms.

Interpretation Introduction

(b)

Interpretation:

The functions of time that will appear in y(t) for the given function Y(s)=2s(s2+4s+3) is to be determined. Also, whether the function y(t) is oscillatory or have constant value for large values of t is to be determined.

Concept introduction:

For a function f(t), the Laplace transform is given by,

F(s)=L[f(t)]=0f(f)estdt

Here, F(s) represents the Laplace transform, s is a variable which is complex and independent, f(t) is any function of time which is being transformed, and L is the operator which is defined by an integral.

f(t) is calculated by taking inverse Laplace transform of the function F(s).

PFE is the partial fraction expansion is the method of expanding the denominator of a fraction into simpler terms.

Interpretation Introduction

(c)

Interpretation:

The functions of time that will appear in y(t) for the given function Y(s)=2s(s2+4s+4) is to be determined. Also, whether the function y(t) is oscillatory or have constant value for large values of t is to be determined.

Concept introduction:

For a function f(t), the Laplace transform is given by,

F(s)=L[f(t)]=0f(f)estdt

Here, F(s) represents the Laplace transform, s is a variable which is complex and independent, f(t) is any function of time which is being transformed, and L is the operator which is defined by an integral.

f(t) is calculated by taking inverse Laplace transform of the function F(s).

PFE is the partial fraction expansion is the method of expanding the denominator of a fraction into simpler terms.

Interpretation Introduction

(d)

Interpretation:

The functions of time that will appear in y(t) for the given function Y(s)=2s(s2+4s+8) is to be determined. Also, whether the function y(t) is oscillatory or have constant value for large values of t is to be determined.

Concept introduction:

For a function f(t), the Laplace transform is given by,

F(s)=L[f(t)]=0f(f)estdt

Here, F(s) represents the Laplace transform, s is a variable which is complex and independent, f(t) is any function of time which is being transformed, and L is the operator which is defined by an integral.

f(t) is calculated by taking inverse Laplace transform of the function F(s).

PFE is the partial fraction expansion is the method of expanding the denominator of a fraction into simpler terms.

Interpretation Introduction

(e)

Interpretation:

The functions of time that will appear in y(t) for the given function Y(s)=2(s+1)s(s2+4) is to be determined. Also, whether the function y(t) is oscillatory or have constant value for large values of t is to be determined.

Concept introduction:

For a function f(t), the Laplace transform is given by,

F(s)=L[f(t)]=0f(f)estdt

Here, F(s) represents the Laplace transform, s is a variable which is complex and independent, f(t) is any function of time which is being transformed, and L is the operator which is defined by an integral.

f(t) is calculated by taking inverse Laplace transform of the function F(s).

PFE is the partial fraction expansion is the method of expanding the denominator of a fraction into simpler terms.

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