Is a vertically bouncing ball an example of oscillatory motion? Of simple harmonic motion ? Explain.

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Answer 1

Textbook Question

Chapter 13, Problem 1FTD

Is a vertically bouncing ball an example of oscillatory motion? Of simple harmonic motion? Explain.

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.

Expert Solution & Answer

To determine

Whether a vertically bouncing ball an example of oscillatory and simple harmonic motion.

Answer to Problem 1FTD

A vertically bouncing ball an example of oscillatory as the ball goes back and forth an equilibrium point and also of simple harmonic motion for small amplitude as the restoring force will be proportional to the displacement alone.

Explanation of Solution

An oscillatory motion is one in which a system goes back and forth an equilibrium point. A simple harmonic motion is one in which the restoring force is proportional to the displacement of the system.

When a ball is made to move in the vertical direction, the ball bounces of the ground and comes back to the ground. This happens in the same way as an oscillatory motion. The ball moves to and fro with respect to the ground and ergo, the vertically bouncing ball qualifies as an oscillatory system.

For a simple harmonic oscillator the restoring force acting on the material is proportional to the displacement. When the ball bounces vertically with low amplitude the ball will have a restoring force that is proportional to the amplitude which will keep it bouncing. Therefore, the bouncing ball will qualify as a simple harmonic oscillator when the amplitude of bouncing is low.

Conclusion:

Therefore, a vertically bouncing ball an example of oscillatory as the ball goes back and forth an equilibrium point and also of simple harmonic motion for small amplitude as the restoring force will be proportional to the displacement alone.

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1.62 On a training flight, a Figure P1.62 student pilot flies from Lincoln, Nebraska, to Clarinda, Iowa, next to St. Joseph, Missouri, and then to Manhattan, Kansas (Fig. P1.62). The directions are shown relative to north: 0° is north, 90° is east, 180° is south, and 270° is west. Use the method of components to find (a) the distance she has to fly from Manhattan to get back to Lincoln, and (b) the direction (relative to north) she must fly to get there. Illustrate your solutions with a vector diagram. IOWA 147 km Lincoln 85° Clarinda 106 km 167° St. Joseph NEBRASKA Manhattan 166 km 235° S KANSAS MISSOURI

Answer 2

Textbook Question

Chapter 13, Problem 1FTD

Is a vertically bouncing ball an example of oscillatory motion? Of simple harmonic motion? Explain.

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.

Expert Solution & Answer

To determine

Whether a vertically bouncing ball an example of oscillatory and simple harmonic motion.

Answer to Problem 1FTD

A vertically bouncing ball an example of oscillatory as the ball goes back and forth an equilibrium point and also of simple harmonic motion for small amplitude as the restoring force will be proportional to the displacement alone.

Explanation of Solution

An oscillatory motion is one in which a system goes back and forth an equilibrium point. A simple harmonic motion is one in which the restoring force is proportional to the displacement of the system.

When a ball is made to move in the vertical direction, the ball bounces of the ground and comes back to the ground. This happens in the same way as an oscillatory motion. The ball moves to and fro with respect to the ground and ergo, the vertically bouncing ball qualifies as an oscillatory system.

For a simple harmonic oscillator the restoring force acting on the material is proportional to the displacement. When the ball bounces vertically with low amplitude the ball will have a restoring force that is proportional to the amplitude which will keep it bouncing. Therefore, the bouncing ball will qualify as a simple harmonic oscillator when the amplitude of bouncing is low.

Conclusion:

Therefore, a vertically bouncing ball an example of oscillatory as the ball goes back and forth an equilibrium point and also of simple harmonic motion for small amplitude as the restoring force will be proportional to the displacement alone.

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Answer 3

Textbook Question

Chapter 13, Problem 1FTD

Is a vertically bouncing ball an example of oscillatory motion? Of simple harmonic motion? Explain.

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.

Expert Solution & Answer

To determine

Whether a vertically bouncing ball an example of oscillatory and simple harmonic motion.

Answer to Problem 1FTD

A vertically bouncing ball an example of oscillatory as the ball goes back and forth an equilibrium point and also of simple harmonic motion for small amplitude as the restoring force will be proportional to the displacement alone.

Explanation of Solution

An oscillatory motion is one in which a system goes back and forth an equilibrium point. A simple harmonic motion is one in which the restoring force is proportional to the displacement of the system.

When a ball is made to move in the vertical direction, the ball bounces of the ground and comes back to the ground. This happens in the same way as an oscillatory motion. The ball moves to and fro with respect to the ground and ergo, the vertically bouncing ball qualifies as an oscillatory system.

For a simple harmonic oscillator the restoring force acting on the material is proportional to the displacement. When the ball bounces vertically with low amplitude the ball will have a restoring force that is proportional to the amplitude which will keep it bouncing. Therefore, the bouncing ball will qualify as a simple harmonic oscillator when the amplitude of bouncing is low.

Conclusion:

Therefore, a vertically bouncing ball an example of oscillatory as the ball goes back and forth an equilibrium point and also of simple harmonic motion for small amplitude as the restoring force will be proportional to the displacement alone.

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Answer 4

Textbook Question

Chapter 13, Problem 1FTD

Is a vertically bouncing ball an example of oscillatory motion? Of simple harmonic motion? Explain.

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.

Expert Solution & Answer

To determine

Whether a vertically bouncing ball an example of oscillatory and simple harmonic motion.

Answer to Problem 1FTD

A vertically bouncing ball an example of oscillatory as the ball goes back and forth an equilibrium point and also of simple harmonic motion for small amplitude as the restoring force will be proportional to the displacement alone.

Explanation of Solution

An oscillatory motion is one in which a system goes back and forth an equilibrium point. A simple harmonic motion is one in which the restoring force is proportional to the displacement of the system.

When a ball is made to move in the vertical direction, the ball bounces of the ground and comes back to the ground. This happens in the same way as an oscillatory motion. The ball moves to and fro with respect to the ground and ergo, the vertically bouncing ball qualifies as an oscillatory system.

For a simple harmonic oscillator the restoring force acting on the material is proportional to the displacement. When the ball bounces vertically with low amplitude the ball will have a restoring force that is proportional to the amplitude which will keep it bouncing. Therefore, the bouncing ball will qualify as a simple harmonic oscillator when the amplitude of bouncing is low.

Conclusion:

Therefore, a vertically bouncing ball an example of oscillatory as the ball goes back and forth an equilibrium point and also of simple harmonic motion for small amplitude as the restoring force will be proportional to the displacement alone.

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

Expert Solution & Answer

To determine

Whether a vertically bouncing ball an example of oscillatory and simple harmonic motion.

Answer to Problem 1FTD

A vertically bouncing ball an example of oscillatory as the ball goes back and forth an equilibrium point and also of simple harmonic motion for small amplitude as the restoring force will be proportional to the displacement alone.

Explanation of Solution

An oscillatory motion is one in which a system goes back and forth an equilibrium point. A simple harmonic motion is one in which the restoring force is proportional to the displacement of the system.

When a ball is made to move in the vertical direction, the ball bounces of the ground and comes back to the ground. This happens in the same way as an oscillatory motion. The ball moves to and fro with respect to the ground and ergo, the vertically bouncing ball qualifies as an oscillatory system.

For a simple harmonic oscillator the restoring force acting on the material is proportional to the displacement. When the ball bounces vertically with low amplitude the ball will have a restoring force that is proportional to the amplitude which will keep it bouncing. Therefore, the bouncing ball will qualify as a simple harmonic oscillator when the amplitude of bouncing is low.

Conclusion:

Therefore, a vertically bouncing ball an example of oscillatory as the ball goes back and forth an equilibrium point and also of simple harmonic motion for small amplitude as the restoring force will be proportional to the displacement alone.

Answer 8

Expert Solution & Answer

To determine

Whether a vertically bouncing ball an example of oscillatory and simple harmonic motion.

Answer to Problem 1FTD

A vertically bouncing ball an example of oscillatory as the ball goes back and forth an equilibrium point and also of simple harmonic motion for small amplitude as the restoring force will be proportional to the displacement alone.

Explanation of Solution

An oscillatory motion is one in which a system goes back and forth an equilibrium point. A simple harmonic motion is one in which the restoring force is proportional to the displacement of the system.

When a ball is made to move in the vertical direction, the ball bounces of the ground and comes back to the ground. This happens in the same way as an oscillatory motion. The ball moves to and fro with respect to the ground and ergo, the vertically bouncing ball qualifies as an oscillatory system.

For a simple harmonic oscillator the restoring force acting on the material is proportional to the displacement. When the ball bounces vertically with low amplitude the ball will have a restoring force that is proportional to the amplitude which will keep it bouncing. Therefore, the bouncing ball will qualify as a simple harmonic oscillator when the amplitude of bouncing is low.

Conclusion:

Therefore, a vertically bouncing ball an example of oscillatory as the ball goes back and forth an equilibrium point and also of simple harmonic motion for small amplitude as the restoring force will be proportional to the displacement alone.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

To determine

Whether a vertically bouncing ball an example of oscillatory and simple harmonic motion.

Answer 12

Answer to Problem 1FTD

A vertically bouncing ball an example of oscillatory as the ball goes back and forth an equilibrium point and also of simple harmonic motion for small amplitude as the restoring force will be proportional to the displacement alone.

Answer 13

Explanation of Solution

An oscillatory motion is one in which a system goes back and forth an equilibrium point. A simple harmonic motion is one in which the restoring force is proportional to the displacement of the system.

When a ball is made to move in the vertical direction, the ball bounces of the ground and comes back to the ground. This happens in the same way as an oscillatory motion. The ball moves to and fro with respect to the ground and ergo, the vertically bouncing ball qualifies as an oscillatory system.

For a simple harmonic oscillator the restoring force acting on the material is proportional to the displacement. When the ball bounces vertically with low amplitude the ball will have a restoring force that is proportional to the amplitude which will keep it bouncing. Therefore, the bouncing ball will qualify as a simple harmonic oscillator when the amplitude of bouncing is low.

Conclusion:

Therefore, a vertically bouncing ball an example of oscillatory as the ball goes back and forth an equilibrium point and also of simple harmonic motion for small amplitude as the restoring force will be proportional to the displacement alone.