To sketch θ ˙ vs t for θ' = γ - sinθ at different values of γ including limiting cases γ ≈ 1, γ >> 1 . Concept Introduction: Overdamped pendulum is an example of a non-uniform oscillator. The motion of an overdamped pendulum is governed by θ' = γ - sinθ , where θ is the angle between the pendulum and the downward vertical and γ is the ratio of applied torque to the maximum gravitational torque.

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Answer 1

Question

Chapter 4.4, Problem 3E

Interpretation Introduction

Interpretation:

To sketch θ˙ vs t for θ' = γ - sinθ at different values of γ including limiting cases γ≈1, γ >> 1.

Concept Introduction:

Overdamped pendulum is an example of a non-uniform oscillator.

The motion of an overdamped pendulum is governed by θ' = γ - sinθ, where θ is the angle between the pendulum and the downward vertical and γ is the ratio of applied torque to the maximum gravitational torque.

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Answer 2

Question

Chapter 4.4, Problem 3E

Interpretation Introduction

Interpretation:

To sketch θ˙ vs t for θ' = γ - sinθ at different values of γ including limiting cases γ≈1, γ >> 1.

Concept Introduction:

Overdamped pendulum is an example of a non-uniform oscillator.

The motion of an overdamped pendulum is governed by θ' = γ - sinθ, where θ is the angle between the pendulum and the downward vertical and γ is the ratio of applied torque to the maximum gravitational torque.

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Answer 3

Question

Chapter 4.4, Problem 3E

Interpretation Introduction

Interpretation:

To sketch θ˙ vs t for θ' = γ - sinθ at different values of γ including limiting cases γ≈1, γ >> 1.

Concept Introduction:

Overdamped pendulum is an example of a non-uniform oscillator.

The motion of an overdamped pendulum is governed by θ' = γ - sinθ, where θ is the angle between the pendulum and the downward vertical and γ is the ratio of applied torque to the maximum gravitational torque.

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Answer 4

Question

Chapter 4.4, Problem 3E

Interpretation Introduction

Interpretation:

To sketch θ˙ vs t for θ' = γ - sinθ at different values of γ including limiting cases γ≈1, γ >> 1.

Concept Introduction:

Overdamped pendulum is an example of a non-uniform oscillator.

The motion of an overdamped pendulum is governed by θ' = γ - sinθ, where θ is the angle between the pendulum and the downward vertical and γ is the ratio of applied torque to the maximum gravitational torque.

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Answer 5

Chapter 4.4, Problem 3E

Interpretation Introduction

Interpretation:

To sketch θ˙ vs t for θ' = γ - sinθ at different values of γ including limiting cases γ≈1, γ >> 1.

Concept Introduction:

Overdamped pendulum is an example of a non-uniform oscillator.

The motion of an overdamped pendulum is governed by θ' = γ - sinθ, where θ is the angle between the pendulum and the downward vertical and γ is the ratio of applied torque to the maximum gravitational torque.

Answer 6

Chapter 4.4, Problem 3E

Interpretation Introduction

Interpretation:

To sketch θ˙ vs t for θ' = γ - sinθ at different values of γ including limiting cases γ≈1, γ >> 1.

Concept Introduction:

Overdamped pendulum is an example of a non-uniform oscillator.

The motion of an overdamped pendulum is governed by θ' = γ - sinθ, where θ is the angle between the pendulum and the downward vertical and γ is the ratio of applied torque to the maximum gravitational torque.

Answer 7

Chapter 4.4, Problem 3E

Interpretation Introduction

Interpretation:

To sketch θ˙ vs t for θ' = γ - sinθ at different values of γ including limiting cases γ≈1, γ >> 1.

Concept Introduction:

Overdamped pendulum is an example of a non-uniform oscillator.

The motion of an overdamped pendulum is governed by θ' = γ - sinθ, where θ is the angle between the pendulum and the downward vertical and γ is the ratio of applied torque to the maximum gravitational torque.

Answer 8

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Answer 9

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Answer 10

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Answer 11

Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E Ch. 4.1 - Prob. 7E Ch. 4.1 - Prob. 8E Ch. 4.1 - Prob. 9E Ch. 4.2 - Prob. 1E

Solution Summary: The author illustrates how the overdamped pendulum is an example of a non-uniform oscillator.

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