It is to be proved that, the solutions of x ˙ = f(x) cannot oscillate using the existence of a potential function V(x) . Concept Introduction: V(t) is a decreasing function of time. So, the potential of a particle decreases along its path and the particle always tends to move toward lower potential. The potential of the particle remains constant only at equilibrium.

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Answer 1

Question

Chapter 2.7, Problem 7E

Interpretation Introduction

Interpretation:

It is to be proved that, the solutions of x˙ = f(x) cannot oscillate using the existence of a potential function V(x).

Concept Introduction:

V(t) is a decreasing function of time. So, the potential of a particle decreases along its path and the particle always tends to move toward lower potential.

The potential of the particle remains constant only at equilibrium.

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Answer 2

Question

Chapter 2.7, Problem 7E

Interpretation Introduction

Interpretation:

It is to be proved that, the solutions of x˙ = f(x) cannot oscillate using the existence of a potential function V(x).

Concept Introduction:

V(t) is a decreasing function of time. So, the potential of a particle decreases along its path and the particle always tends to move toward lower potential.

The potential of the particle remains constant only at equilibrium.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 2.7, Problem 7E

Interpretation Introduction

Interpretation:

It is to be proved that, the solutions of x˙ = f(x) cannot oscillate using the existence of a potential function V(x).

Concept Introduction:

V(t) is a decreasing function of time. So, the potential of a particle decreases along its path and the particle always tends to move toward lower potential.

The potential of the particle remains constant only at equilibrium.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 2.7, Problem 7E

Interpretation Introduction

Interpretation:

It is to be proved that, the solutions of x˙ = f(x) cannot oscillate using the existence of a potential function V(x).

Concept Introduction:

V(t) is a decreasing function of time. So, the potential of a particle decreases along its path and the particle always tends to move toward lower potential.

The potential of the particle remains constant only at equilibrium.

Expert Solution & Answer

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Answer 5

Chapter 2.7, Problem 7E

Interpretation Introduction

Interpretation:

It is to be proved that, the solutions of x˙ = f(x) cannot oscillate using the existence of a potential function V(x).

Concept Introduction:

V(t) is a decreasing function of time. So, the potential of a particle decreases along its path and the particle always tends to move toward lower potential.

The potential of the particle remains constant only at equilibrium.

Answer 6

Chapter 2.7, Problem 7E

Interpretation Introduction

Interpretation:

It is to be proved that, the solutions of x˙ = f(x) cannot oscillate using the existence of a potential function V(x).

Concept Introduction:

V(t) is a decreasing function of time. So, the potential of a particle decreases along its path and the particle always tends to move toward lower potential.

The potential of the particle remains constant only at equilibrium.

Answer 7

Chapter 2.7, Problem 7E

Interpretation Introduction

Interpretation:

It is to be proved that, the solutions of x˙ = f(x) cannot oscillate using the existence of a potential function V(x).

Concept Introduction:

V(t) is a decreasing function of time. So, the potential of a particle decreases along its path and the particle always tends to move toward lower potential.

The potential of the particle remains constant only at equilibrium.

Answer 8

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Answer 9

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Answer 10

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Answer 11

Ch. 2.1 - Prob. 1E Ch. 2.1 - Prob. 2E Ch. 2.1 - Prob. 3E Ch. 2.1 - Prob. 4E Ch. 2.1 - Prob. 5E Ch. 2.2 - Prob. 1E Ch. 2.2 - Prob. 2E Ch. 2.2 - Prob. 3E Ch. 2.2 - Prob. 4E Ch. 2.2 - Prob. 5E

Solution Summary: The author proves that the solutions of stackreldotx = f(x) cannot oscillate using the existence of a potential function.

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