Which of the following statements is not true regarding a mass–spring system that moves with simple harmonic motion in the absence of friction? (a) The total energy of the system remains constant. (b) The energy of the system is continually transformed between kinetic and potential energy. (c) The total energy of the system is proportional to the square of the amplitude. (d) The potential energy stored in the system is greatest when the mass passes through the equilibrium position. (e) The velocity of the oscillating mass has its maximum value when the mass passes through the equilibrium position.

Question

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Answer 1

Textbook Question

Chapter 12, Problem 1OQ

Which of the following statements is not true regarding a mass–spring system that moves with simple harmonic motion in the absence of friction? (a) The total energy of the system remains constant. (b) The energy of the system is continually transformed between kinetic and potential energy. (c) The total energy of the system is proportional to the square of the amplitude. (d) The potential energy stored in the system is greatest when the mass passes through the equilibrium position. (e) The velocity of the oscillating mass has its maximum value when the mass passes through the equilibrium position.

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

The statement which is not true regarding a mass spring system that moves with simple harmonic motion in the absence of friction.

Answer to Problem 1OQ

Option (d), the potential energy stored in the system is greatest when the mass passes through the equilibrium position.

Explanation of Solution

Write the expression for the potential energy stored in the system.

PE=12kx2 (I)

Here, k is the spring constant, x is the distance traveled.

At the equilibrium position, x is zero so that equation (I) changes to,

PEs=12k(0)=0 (II)

From equation (II) it is show that the potential energy is minimum at the equilibrium position. Since the total energy is constant, minimum potential energy will gives a maximum kinetic energy.

Conclusion:

Since potential energy is minimum at equilibrium position, option (d) is false statement.

According to the conservation of energy, the total energy will be a constant, thus, option (a) is not a false statement.

To make energy as a constant, the energy of the system is continually transformed between kinetic and potential energy. Thus, option (b) is not a false statement.

The total energy of the system is proportional to the square of the amplitude Thus, option (c) is not a false statement.

The velocity of the oscillating object will have maximum value when it is passing through the equilibrium position, thus option (e) is incorrect.

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Answer 2

Textbook Question

Chapter 12, Problem 1OQ

Which of the following statements is not true regarding a mass–spring system that moves with simple harmonic motion in the absence of friction? (a) The total energy of the system remains constant. (b) The energy of the system is continually transformed between kinetic and potential energy. (c) The total energy of the system is proportional to the square of the amplitude. (d) The potential energy stored in the system is greatest when the mass passes through the equilibrium position. (e) The velocity of the oscillating mass has its maximum value when the mass passes through the equilibrium position.

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

The statement which is not true regarding a mass spring system that moves with simple harmonic motion in the absence of friction.

Answer to Problem 1OQ

Option (d), the potential energy stored in the system is greatest when the mass passes through the equilibrium position.

Explanation of Solution

Write the expression for the potential energy stored in the system.

PE=12kx2 (I)

Here, k is the spring constant, x is the distance traveled.

At the equilibrium position, x is zero so that equation (I) changes to,

PEs=12k(0)=0 (II)

From equation (II) it is show that the potential energy is minimum at the equilibrium position. Since the total energy is constant, minimum potential energy will gives a maximum kinetic energy.

Conclusion:

Since potential energy is minimum at equilibrium position, option (d) is false statement.

According to the conservation of energy, the total energy will be a constant, thus, option (a) is not a false statement.

To make energy as a constant, the energy of the system is continually transformed between kinetic and potential energy. Thus, option (b) is not a false statement.

The total energy of the system is proportional to the square of the amplitude Thus, option (c) is not a false statement.

The velocity of the oscillating object will have maximum value when it is passing through the equilibrium position, thus option (e) is incorrect.

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Answer 3

Textbook Question

Chapter 12, Problem 1OQ

Which of the following statements is not true regarding a mass–spring system that moves with simple harmonic motion in the absence of friction? (a) The total energy of the system remains constant. (b) The energy of the system is continually transformed between kinetic and potential energy. (c) The total energy of the system is proportional to the square of the amplitude. (d) The potential energy stored in the system is greatest when the mass passes through the equilibrium position. (e) The velocity of the oscillating mass has its maximum value when the mass passes through the equilibrium position.

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

The statement which is not true regarding a mass spring system that moves with simple harmonic motion in the absence of friction.

Answer to Problem 1OQ

Option (d), the potential energy stored in the system is greatest when the mass passes through the equilibrium position.

Explanation of Solution

Write the expression for the potential energy stored in the system.

PE=12kx2 (I)

Here, k is the spring constant, x is the distance traveled.

At the equilibrium position, x is zero so that equation (I) changes to,

PEs=12k(0)=0 (II)

From equation (II) it is show that the potential energy is minimum at the equilibrium position. Since the total energy is constant, minimum potential energy will gives a maximum kinetic energy.

Conclusion:

Since potential energy is minimum at equilibrium position, option (d) is false statement.

According to the conservation of energy, the total energy will be a constant, thus, option (a) is not a false statement.

To make energy as a constant, the energy of the system is continually transformed between kinetic and potential energy. Thus, option (b) is not a false statement.

The total energy of the system is proportional to the square of the amplitude Thus, option (c) is not a false statement.

The velocity of the oscillating object will have maximum value when it is passing through the equilibrium position, thus option (e) is incorrect.

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Answer 4

Textbook Question

Chapter 12, Problem 1OQ

Which of the following statements is not true regarding a mass–spring system that moves with simple harmonic motion in the absence of friction? (a) The total energy of the system remains constant. (b) The energy of the system is continually transformed between kinetic and potential energy. (c) The total energy of the system is proportional to the square of the amplitude. (d) The potential energy stored in the system is greatest when the mass passes through the equilibrium position. (e) The velocity of the oscillating mass has its maximum value when the mass passes through the equilibrium position.

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

The statement which is not true regarding a mass spring system that moves with simple harmonic motion in the absence of friction.

Answer to Problem 1OQ

Option (d), the potential energy stored in the system is greatest when the mass passes through the equilibrium position.

Explanation of Solution

Write the expression for the potential energy stored in the system.

PE=12kx2 (I)

Here, k is the spring constant, x is the distance traveled.

At the equilibrium position, x is zero so that equation (I) changes to,

PEs=12k(0)=0 (II)

From equation (II) it is show that the potential energy is minimum at the equilibrium position. Since the total energy is constant, minimum potential energy will gives a maximum kinetic energy.

Conclusion:

Since potential energy is minimum at equilibrium position, option (d) is false statement.

According to the conservation of energy, the total energy will be a constant, thus, option (a) is not a false statement.

To make energy as a constant, the energy of the system is continually transformed between kinetic and potential energy. Thus, option (b) is not a false statement.

The total energy of the system is proportional to the square of the amplitude Thus, option (c) is not a false statement.

The velocity of the oscillating object will have maximum value when it is passing through the equilibrium position, thus option (e) is incorrect.

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

Expert Solution & Answer

To determine

The statement which is not true regarding a mass spring system that moves with simple harmonic motion in the absence of friction.

Answer to Problem 1OQ

Option (d), the potential energy stored in the system is greatest when the mass passes through the equilibrium position.

Explanation of Solution

Write the expression for the potential energy stored in the system.

PE=12kx2 (I)

Here, k is the spring constant, x is the distance traveled.

At the equilibrium position, x is zero so that equation (I) changes to,

PEs=12k(0)=0 (II)

From equation (II) it is show that the potential energy is minimum at the equilibrium position. Since the total energy is constant, minimum potential energy will gives a maximum kinetic energy.

Conclusion:

Since potential energy is minimum at equilibrium position, option (d) is false statement.

According to the conservation of energy, the total energy will be a constant, thus, option (a) is not a false statement.

To make energy as a constant, the energy of the system is continually transformed between kinetic and potential energy. Thus, option (b) is not a false statement.

The total energy of the system is proportional to the square of the amplitude Thus, option (c) is not a false statement.

The velocity of the oscillating object will have maximum value when it is passing through the equilibrium position, thus option (e) is incorrect.

Answer 8

Expert Solution & Answer

To determine

The statement which is not true regarding a mass spring system that moves with simple harmonic motion in the absence of friction.

Answer to Problem 1OQ

Option (d), the potential energy stored in the system is greatest when the mass passes through the equilibrium position.

Explanation of Solution

Write the expression for the potential energy stored in the system.

PE=12kx2 (I)

Here, k is the spring constant, x is the distance traveled.

At the equilibrium position, x is zero so that equation (I) changes to,

PEs=12k(0)=0 (II)

From equation (II) it is show that the potential energy is minimum at the equilibrium position. Since the total energy is constant, minimum potential energy will gives a maximum kinetic energy.

Conclusion:

Since potential energy is minimum at equilibrium position, option (d) is false statement.

According to the conservation of energy, the total energy will be a constant, thus, option (a) is not a false statement.

To make energy as a constant, the energy of the system is continually transformed between kinetic and potential energy. Thus, option (b) is not a false statement.

The total energy of the system is proportional to the square of the amplitude Thus, option (c) is not a false statement.

The velocity of the oscillating object will have maximum value when it is passing through the equilibrium position, thus option (e) is incorrect.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

To determine

The statement which is not true regarding a mass spring system that moves with simple harmonic motion in the absence of friction.

Answer 12

Answer to Problem 1OQ

Option (d), the potential energy stored in the system is greatest when the mass passes through the equilibrium position.

Answer 13

Explanation of Solution

Write the expression for the potential energy stored in the system.

PE=12kx2 (I)

Here, k is the spring constant, x is the distance traveled.

At the equilibrium position, x is zero so that equation (I) changes to,

PEs=12k(0)=0 (II)

From equation (II) it is show that the potential energy is minimum at the equilibrium position. Since the total energy is constant, minimum potential energy will gives a maximum kinetic energy.

Conclusion:

Since potential energy is minimum at equilibrium position, option (d) is false statement.

According to the conservation of energy, the total energy will be a constant, thus, option (a) is not a false statement.

To make energy as a constant, the energy of the system is continually transformed between kinetic and potential energy. Thus, option (b) is not a false statement.

The total energy of the system is proportional to the square of the amplitude Thus, option (c) is not a false statement.

The velocity of the oscillating object will have maximum value when it is passing through the equilibrium position, thus option (e) is incorrect.