If the acceleration of a simple harmonic oscillator is ever zero.

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Answer 1

Question

Definition Definition Special type of oscillation where the force of restoration is directly proportional to the displacement of the object from its mean or initial position. If an object is in motion such that the acceleration of the object is directly proportional to its displacement (which helps the moving object return to its resting position) then the object is said to undergo a simple harmonic motion. An object undergoing SHM always moves like a wave.

Chapter 11, Problem 1Q

To determine

If the acceleration of a simple harmonic oscillator is ever zero.

Expert Solution & Answer

Answer to Problem 1Q

Solution:

The acceleration is zero at the place where displacement is equal to zero and when the velocity is at its maximum, at the equilibrium position.

Explanation of Solution

The acceleration is zero at the place where displacement is equal to zero.

At the point in the centre, the acceleration drops to zero and changes direction when the velocity changes from increasing to decreasing.

The acceleration is zero as it crosses the equilibrium point.

The acceleration is zero when the velocity is at its maximum, that is, at the equilibrium position. Since the force and hence the acceleration always acts towards the equilibrium position (because it is a restorative force), then the force and acceleration must change their sign as the mass crosses the equilibrium point, and therefore must be zero instantaneously at the equilibrium point. Acceleration changes during simple harmonic motion and it is zero at equilibrium.

The acceleration also oscillates in simple harmonic motion. If you consider a mass on a spring, when the displacement is zero the acceleration is also zero, because the spring applies no force. When the displacement is maximum, the acceleration is maximum, because the spring applies maximum force; the force applied by the spring is in the opposite direction as the displacement. The acceleration is given by

Physics: Principles with Applications, Chapter 11, Problem 1Q , additional homework tip 1

So, the maximum acceleration is Physics: Principles with Applications, Chapter 11, Problem 1Q , additional homework tip 2

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Answer 2

Question

Definition Definition Special type of oscillation where the force of restoration is directly proportional to the displacement of the object from its mean or initial position. If an object is in motion such that the acceleration of the object is directly proportional to its displacement (which helps the moving object return to its resting position) then the object is said to undergo a simple harmonic motion. An object undergoing SHM always moves like a wave.

Chapter 11, Problem 1Q

To determine

If the acceleration of a simple harmonic oscillator is ever zero.

Expert Solution & Answer

Answer to Problem 1Q

Solution:

The acceleration is zero at the place where displacement is equal to zero and when the velocity is at its maximum, at the equilibrium position.

Explanation of Solution

The acceleration is zero at the place where displacement is equal to zero.

At the point in the centre, the acceleration drops to zero and changes direction when the velocity changes from increasing to decreasing.

The acceleration is zero as it crosses the equilibrium point.

The acceleration is zero when the velocity is at its maximum, that is, at the equilibrium position. Since the force and hence the acceleration always acts towards the equilibrium position (because it is a restorative force), then the force and acceleration must change their sign as the mass crosses the equilibrium point, and therefore must be zero instantaneously at the equilibrium point. Acceleration changes during simple harmonic motion and it is zero at equilibrium.

The acceleration also oscillates in simple harmonic motion. If you consider a mass on a spring, when the displacement is zero the acceleration is also zero, because the spring applies no force. When the displacement is maximum, the acceleration is maximum, because the spring applies maximum force; the force applied by the spring is in the opposite direction as the displacement. The acceleration is given by

Physics: Principles with Applications, Chapter 11, Problem 1Q , additional homework tip 1

So, the maximum acceleration is Physics: Principles with Applications, Chapter 11, Problem 1Q , additional homework tip 2

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Answer 3

Question

Definition Definition Special type of oscillation where the force of restoration is directly proportional to the displacement of the object from its mean or initial position. If an object is in motion such that the acceleration of the object is directly proportional to its displacement (which helps the moving object return to its resting position) then the object is said to undergo a simple harmonic motion. An object undergoing SHM always moves like a wave.

Chapter 11, Problem 1Q

To determine

If the acceleration of a simple harmonic oscillator is ever zero.

Expert Solution & Answer

Answer to Problem 1Q

Solution:

The acceleration is zero at the place where displacement is equal to zero and when the velocity is at its maximum, at the equilibrium position.

Explanation of Solution

The acceleration is zero at the place where displacement is equal to zero.

At the point in the centre, the acceleration drops to zero and changes direction when the velocity changes from increasing to decreasing.

The acceleration is zero as it crosses the equilibrium point.

The acceleration is zero when the velocity is at its maximum, that is, at the equilibrium position. Since the force and hence the acceleration always acts towards the equilibrium position (because it is a restorative force), then the force and acceleration must change their sign as the mass crosses the equilibrium point, and therefore must be zero instantaneously at the equilibrium point. Acceleration changes during simple harmonic motion and it is zero at equilibrium.

The acceleration also oscillates in simple harmonic motion. If you consider a mass on a spring, when the displacement is zero the acceleration is also zero, because the spring applies no force. When the displacement is maximum, the acceleration is maximum, because the spring applies maximum force; the force applied by the spring is in the opposite direction as the displacement. The acceleration is given by

Physics: Principles with Applications, Chapter 11, Problem 1Q , additional homework tip 1

So, the maximum acceleration is Physics: Principles with Applications, Chapter 11, Problem 1Q , additional homework tip 2

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Answer 4

Question

Definition Definition Special type of oscillation where the force of restoration is directly proportional to the displacement of the object from its mean or initial position. If an object is in motion such that the acceleration of the object is directly proportional to its displacement (which helps the moving object return to its resting position) then the object is said to undergo a simple harmonic motion. An object undergoing SHM always moves like a wave.

Chapter 11, Problem 1Q

To determine

If the acceleration of a simple harmonic oscillator is ever zero.

Expert Solution & Answer

Answer to Problem 1Q

Solution:

The acceleration is zero at the place where displacement is equal to zero and when the velocity is at its maximum, at the equilibrium position.

Explanation of Solution

The acceleration is zero at the place where displacement is equal to zero.

At the point in the centre, the acceleration drops to zero and changes direction when the velocity changes from increasing to decreasing.

The acceleration is zero as it crosses the equilibrium point.

The acceleration is zero when the velocity is at its maximum, that is, at the equilibrium position. Since the force and hence the acceleration always acts towards the equilibrium position (because it is a restorative force), then the force and acceleration must change their sign as the mass crosses the equilibrium point, and therefore must be zero instantaneously at the equilibrium point. Acceleration changes during simple harmonic motion and it is zero at equilibrium.

The acceleration also oscillates in simple harmonic motion. If you consider a mass on a spring, when the displacement is zero the acceleration is also zero, because the spring applies no force. When the displacement is maximum, the acceleration is maximum, because the spring applies maximum force; the force applied by the spring is in the opposite direction as the displacement. The acceleration is given by

Physics: Principles with Applications, Chapter 11, Problem 1Q , additional homework tip 1

So, the maximum acceleration is Physics: Principles with Applications, Chapter 11, Problem 1Q , additional homework tip 2

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Answer 5

Chapter 11, Problem 1Q

To determine

If the acceleration of a simple harmonic oscillator is ever zero.

Expert Solution & Answer

Answer to Problem 1Q

Solution:

The acceleration is zero at the place where displacement is equal to zero and when the velocity is at its maximum, at the equilibrium position.

Explanation of Solution

The acceleration is zero at the place where displacement is equal to zero.

At the point in the centre, the acceleration drops to zero and changes direction when the velocity changes from increasing to decreasing.

The acceleration is zero as it crosses the equilibrium point.

The acceleration is zero when the velocity is at its maximum, that is, at the equilibrium position. Since the force and hence the acceleration always acts towards the equilibrium position (because it is a restorative force), then the force and acceleration must change their sign as the mass crosses the equilibrium point, and therefore must be zero instantaneously at the equilibrium point. Acceleration changes during simple harmonic motion and it is zero at equilibrium.

The acceleration also oscillates in simple harmonic motion. If you consider a mass on a spring, when the displacement is zero the acceleration is also zero, because the spring applies no force. When the displacement is maximum, the acceleration is maximum, because the spring applies maximum force; the force applied by the spring is in the opposite direction as the displacement. The acceleration is given by

Physics: Principles with Applications, Chapter 11, Problem 1Q , additional homework tip 1

So, the maximum acceleration is Physics: Principles with Applications, Chapter 11, Problem 1Q , additional homework tip 2

Answer 6

Chapter 11, Problem 1Q

To determine

If the acceleration of a simple harmonic oscillator is ever zero.

Expert Solution & Answer

Answer to Problem 1Q

Solution:

The acceleration is zero at the place where displacement is equal to zero and when the velocity is at its maximum, at the equilibrium position.

Explanation of Solution

The acceleration is zero at the place where displacement is equal to zero.

At the point in the centre, the acceleration drops to zero and changes direction when the velocity changes from increasing to decreasing.

The acceleration is zero as it crosses the equilibrium point.

The acceleration is zero when the velocity is at its maximum, that is, at the equilibrium position. Since the force and hence the acceleration always acts towards the equilibrium position (because it is a restorative force), then the force and acceleration must change their sign as the mass crosses the equilibrium point, and therefore must be zero instantaneously at the equilibrium point. Acceleration changes during simple harmonic motion and it is zero at equilibrium.

The acceleration also oscillates in simple harmonic motion. If you consider a mass on a spring, when the displacement is zero the acceleration is also zero, because the spring applies no force. When the displacement is maximum, the acceleration is maximum, because the spring applies maximum force; the force applied by the spring is in the opposite direction as the displacement. The acceleration is given by

Physics: Principles with Applications, Chapter 11, Problem 1Q , additional homework tip 1

So, the maximum acceleration is Physics: Principles with Applications, Chapter 11, Problem 1Q , additional homework tip 2

Answer 7

Chapter 11, Problem 1Q

To determine

If the acceleration of a simple harmonic oscillator is ever zero.

Answer 8

Expert Solution & Answer

Answer to Problem 1Q

Solution:

The acceleration is zero at the place where displacement is equal to zero and when the velocity is at its maximum, at the equilibrium position.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Explanation of Solution

The acceleration is zero at the place where displacement is equal to zero.

At the point in the centre, the acceleration drops to zero and changes direction when the velocity changes from increasing to decreasing.

The acceleration is zero as it crosses the equilibrium point.

The acceleration is zero when the velocity is at its maximum, that is, at the equilibrium position. Since the force and hence the acceleration always acts towards the equilibrium position (because it is a restorative force), then the force and acceleration must change their sign as the mass crosses the equilibrium point, and therefore must be zero instantaneously at the equilibrium point. Acceleration changes during simple harmonic motion and it is zero at equilibrium.

The acceleration also oscillates in simple harmonic motion. If you consider a mass on a spring, when the displacement is zero the acceleration is also zero, because the spring applies no force. When the displacement is maximum, the acceleration is maximum, because the spring applies maximum force; the force applied by the spring is in the opposite direction as the displacement. The acceleration is given by

Physics: Principles with Applications, Chapter 11, Problem 1Q , additional homework tip 1

So, the maximum acceleration is Physics: Principles with Applications, Chapter 11, Problem 1Q , additional homework tip 2