Whether the statement is true or false.

Question

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Answer 1

Question

Chapter 14, Problem 1P

(a)

To determine

Whether the statement is true or false.

(a)

Expert Solution

Explanation of Solution

Introduction:

Simple harmonic oscillator is any system which when displaced from its equilibrium position, exhibits a restoring force where restoring force is directly proportional to the displacement.

The time period in the simple harmonic oscillator is the time taken to complete full oscillation.

Write the expression for the time period of the simple harmonic oscillator.

T=2πmk

Here, T is the time period of the simple harmonic oscillator, k is the force constant and m is the mass of the particle.

Conclusion:

The time period of a simple harmonic oscillator does not depend on the amplitude. Thus, the statement is not correct.

(b)

To determine

Whether the statement is true or false.

(b)

Expert Solution

Explanation of Solution

Write the expression for the time period of the simple harmonic oscillator.

T=2πmk

The frequency in the simple harmonic oscillator is inversely proportional to the time period.

f∝1T ............. (1)

Here, f is the frequency of the simple harmonic oscillator

Substitute 2πmk for T in equation (1).

f=12π m k f=12πkm

Thus, the frequency of the simple harmonic oscillator does not depend on amplitude, it depends on two factors one is mass and the other is force constant.

Conclusion:

The frequency of the simple harmonic oscillator does not depend on the amplitude. Thus, the statement is correct.

(c)

To determine

Whether the statement is true or false.

(c)

Expert Solution

Explanation of Solution

The condition for the simple harmonic oscillator is that force should be directly proportional to the displacement and the displaced object tends to move in its equilibrium position. The restoring force always acts in the direction opposite to the particle displacement. For any system to be simple harmonic the acceleration of the particle is in the opposite direction from its equilibrium position and acceleration should be proportional to the displacement from the equilibrium position.

Conclusion:

The net force in the particle is one-dimensional motion which is directly proportional to the displacement made by the particle from its equilibrium position. Thus, the statement is correct.

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Answer 2

Question

Chapter 14, Problem 1P

(a)

To determine

Whether the statement is true or false.

(a)

Expert Solution

Explanation of Solution

Introduction:

Simple harmonic oscillator is any system which when displaced from its equilibrium position, exhibits a restoring force where restoring force is directly proportional to the displacement.

The time period in the simple harmonic oscillator is the time taken to complete full oscillation.

Write the expression for the time period of the simple harmonic oscillator.

T=2πmk

Here, T is the time period of the simple harmonic oscillator, k is the force constant and m is the mass of the particle.

Conclusion:

The time period of a simple harmonic oscillator does not depend on the amplitude. Thus, the statement is not correct.

(b)

To determine

Whether the statement is true or false.

(b)

Expert Solution

Explanation of Solution

Write the expression for the time period of the simple harmonic oscillator.

T=2πmk

The frequency in the simple harmonic oscillator is inversely proportional to the time period.

f∝1T ............. (1)

Here, f is the frequency of the simple harmonic oscillator

Substitute 2πmk for T in equation (1).

f=12π m k f=12πkm

Thus, the frequency of the simple harmonic oscillator does not depend on amplitude, it depends on two factors one is mass and the other is force constant.

Conclusion:

The frequency of the simple harmonic oscillator does not depend on the amplitude. Thus, the statement is correct.

(c)

To determine

Whether the statement is true or false.

(c)

Expert Solution

Explanation of Solution

The condition for the simple harmonic oscillator is that force should be directly proportional to the displacement and the displaced object tends to move in its equilibrium position. The restoring force always acts in the direction opposite to the particle displacement. For any system to be simple harmonic the acceleration of the particle is in the opposite direction from its equilibrium position and acceleration should be proportional to the displacement from the equilibrium position.

Conclusion:

The net force in the particle is one-dimensional motion which is directly proportional to the displacement made by the particle from its equilibrium position. Thus, the statement is correct.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Question

Chapter 14, Problem 1P

(a)

To determine

Whether the statement is true or false.

(a)

Expert Solution

Explanation of Solution

Introduction:

Simple harmonic oscillator is any system which when displaced from its equilibrium position, exhibits a restoring force where restoring force is directly proportional to the displacement.

The time period in the simple harmonic oscillator is the time taken to complete full oscillation.

Write the expression for the time period of the simple harmonic oscillator.

T=2πmk

Here, T is the time period of the simple harmonic oscillator, k is the force constant and m is the mass of the particle.

Conclusion:

The time period of a simple harmonic oscillator does not depend on the amplitude. Thus, the statement is not correct.

(b)

To determine

Whether the statement is true or false.

(b)

Expert Solution

Explanation of Solution

Write the expression for the time period of the simple harmonic oscillator.

T=2πmk

The frequency in the simple harmonic oscillator is inversely proportional to the time period.

f∝1T ............. (1)

Here, f is the frequency of the simple harmonic oscillator

Substitute 2πmk for T in equation (1).

f=12π m k f=12πkm

Thus, the frequency of the simple harmonic oscillator does not depend on amplitude, it depends on two factors one is mass and the other is force constant.

Conclusion:

The frequency of the simple harmonic oscillator does not depend on the amplitude. Thus, the statement is correct.

(c)

To determine

Whether the statement is true or false.

(c)

Expert Solution

Explanation of Solution

The condition for the simple harmonic oscillator is that force should be directly proportional to the displacement and the displaced object tends to move in its equilibrium position. The restoring force always acts in the direction opposite to the particle displacement. For any system to be simple harmonic the acceleration of the particle is in the opposite direction from its equilibrium position and acceleration should be proportional to the displacement from the equilibrium position.

Conclusion:

The net force in the particle is one-dimensional motion which is directly proportional to the displacement made by the particle from its equilibrium position. Thus, the statement is correct.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Chapter 14, Problem 1P

(a)

To determine

Whether the statement is true or false.

(a)

Expert Solution

Explanation of Solution

Introduction:

Simple harmonic oscillator is any system which when displaced from its equilibrium position, exhibits a restoring force where restoring force is directly proportional to the displacement.

The time period in the simple harmonic oscillator is the time taken to complete full oscillation.

Write the expression for the time period of the simple harmonic oscillator.

T=2πmk

Here, T is the time period of the simple harmonic oscillator, k is the force constant and m is the mass of the particle.

Conclusion:

The time period of a simple harmonic oscillator does not depend on the amplitude. Thus, the statement is not correct.

(b)

To determine

Whether the statement is true or false.

(b)

Expert Solution

Explanation of Solution

Write the expression for the time period of the simple harmonic oscillator.

T=2πmk

The frequency in the simple harmonic oscillator is inversely proportional to the time period.

f∝1T ............. (1)

Here, f is the frequency of the simple harmonic oscillator

Substitute 2πmk for T in equation (1).

f=12π m k f=12πkm

Thus, the frequency of the simple harmonic oscillator does not depend on amplitude, it depends on two factors one is mass and the other is force constant.

Conclusion:

The frequency of the simple harmonic oscillator does not depend on the amplitude. Thus, the statement is correct.

(c)

To determine

Whether the statement is true or false.

(c)

Expert Solution

Explanation of Solution

The condition for the simple harmonic oscillator is that force should be directly proportional to the displacement and the displaced object tends to move in its equilibrium position. The restoring force always acts in the direction opposite to the particle displacement. For any system to be simple harmonic the acceleration of the particle is in the opposite direction from its equilibrium position and acceleration should be proportional to the displacement from the equilibrium position.

Conclusion:

The net force in the particle is one-dimensional motion which is directly proportional to the displacement made by the particle from its equilibrium position. Thus, the statement is correct.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 14, Problem 1P

(a)

To determine

Whether the statement is true or false.

(a)

Expert Solution

Explanation of Solution

Introduction:

Simple harmonic oscillator is any system which when displaced from its equilibrium position, exhibits a restoring force where restoring force is directly proportional to the displacement.

The time period in the simple harmonic oscillator is the time taken to complete full oscillation.

Write the expression for the time period of the simple harmonic oscillator.

T=2πmk

Here, T is the time period of the simple harmonic oscillator, k is the force constant and m is the mass of the particle.

Conclusion:

The time period of a simple harmonic oscillator does not depend on the amplitude. Thus, the statement is not correct.

(b)

To determine

Whether the statement is true or false.

(b)

Expert Solution

Explanation of Solution

Write the expression for the time period of the simple harmonic oscillator.

T=2πmk

The frequency in the simple harmonic oscillator is inversely proportional to the time period.

f∝1T ............. (1)

Here, f is the frequency of the simple harmonic oscillator

Substitute 2πmk for T in equation (1).

f=12π m k f=12πkm

Thus, the frequency of the simple harmonic oscillator does not depend on amplitude, it depends on two factors one is mass and the other is force constant.

Conclusion:

The frequency of the simple harmonic oscillator does not depend on the amplitude. Thus, the statement is correct.

(c)

To determine

Whether the statement is true or false.

(c)

Expert Solution

Explanation of Solution

The condition for the simple harmonic oscillator is that force should be directly proportional to the displacement and the displaced object tends to move in its equilibrium position. The restoring force always acts in the direction opposite to the particle displacement. For any system to be simple harmonic the acceleration of the particle is in the opposite direction from its equilibrium position and acceleration should be proportional to the displacement from the equilibrium position.

Conclusion:

The net force in the particle is one-dimensional motion which is directly proportional to the displacement made by the particle from its equilibrium position. Thus, the statement is correct.

Answer 6

Chapter 14, Problem 1P

(a)

To determine

Whether the statement is true or false.

(a)

Expert Solution

Explanation of Solution

Introduction:

Simple harmonic oscillator is any system which when displaced from its equilibrium position, exhibits a restoring force where restoring force is directly proportional to the displacement.

The time period in the simple harmonic oscillator is the time taken to complete full oscillation.

Write the expression for the time period of the simple harmonic oscillator.

T=2πmk

Here, T is the time period of the simple harmonic oscillator, k is the force constant and m is the mass of the particle.

Conclusion:

The time period of a simple harmonic oscillator does not depend on the amplitude. Thus, the statement is not correct.

Answer 7

Chapter 14, Problem 1P

(a)

To determine

Whether the statement is true or false.

Answer 8

(a)

Expert Solution

Explanation of Solution

Introduction:

Simple harmonic oscillator is any system which when displaced from its equilibrium position, exhibits a restoring force where restoring force is directly proportional to the displacement.

The time period in the simple harmonic oscillator is the time taken to complete full oscillation.

Write the expression for the time period of the simple harmonic oscillator.

T=2πmk

Here, T is the time period of the simple harmonic oscillator, k is the force constant and m is the mass of the particle.

Conclusion:

The time period of a simple harmonic oscillator does not depend on the amplitude. Thus, the statement is not correct.

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

(b)

To determine

Whether the statement is true or false.

(b)

Expert Solution

Explanation of Solution

Write the expression for the time period of the simple harmonic oscillator.

T=2πmk

The frequency in the simple harmonic oscillator is inversely proportional to the time period.

f∝1T ............. (1)

Here, f is the frequency of the simple harmonic oscillator

Substitute 2πmk for T in equation (1).

f=12π m k f=12πkm

Thus, the frequency of the simple harmonic oscillator does not depend on amplitude, it depends on two factors one is mass and the other is force constant.

Conclusion:

The frequency of the simple harmonic oscillator does not depend on the amplitude. Thus, the statement is correct.

Answer 13

(b)

To determine

Whether the statement is true or false.

Answer 14

(b)

Expert Solution

Explanation of Solution

Write the expression for the time period of the simple harmonic oscillator.

T=2πmk

The frequency in the simple harmonic oscillator is inversely proportional to the time period.

f∝1T ............. (1)

Here, f is the frequency of the simple harmonic oscillator

Substitute 2πmk for T in equation (1).

f=12π m k f=12πkm

Thus, the frequency of the simple harmonic oscillator does not depend on amplitude, it depends on two factors one is mass and the other is force constant.

Conclusion:

The frequency of the simple harmonic oscillator does not depend on the amplitude. Thus, the statement is correct.

Answer 15

(b)

Expert Solution

Answer 16

(b)

Expert Solution

Answer 17

Expert Solution

Answer 18

(c)

To determine

Whether the statement is true or false.

(c)

Expert Solution

Explanation of Solution

The condition for the simple harmonic oscillator is that force should be directly proportional to the displacement and the displaced object tends to move in its equilibrium position. The restoring force always acts in the direction opposite to the particle displacement. For any system to be simple harmonic the acceleration of the particle is in the opposite direction from its equilibrium position and acceleration should be proportional to the displacement from the equilibrium position.

Conclusion:

The net force in the particle is one-dimensional motion which is directly proportional to the displacement made by the particle from its equilibrium position. Thus, the statement is correct.

Answer 19

(c)

To determine

Whether the statement is true or false.

Answer 20

(c)

Expert Solution

Explanation of Solution

The condition for the simple harmonic oscillator is that force should be directly proportional to the displacement and the displaced object tends to move in its equilibrium position. The restoring force always acts in the direction opposite to the particle displacement. For any system to be simple harmonic the acceleration of the particle is in the opposite direction from its equilibrium position and acceleration should be proportional to the displacement from the equilibrium position.

Conclusion:

The net force in the particle is one-dimensional motion which is directly proportional to the displacement made by the particle from its equilibrium position. Thus, the statement is correct.