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AP Physics C: Mechanics Practice Quiz: Energy of Simple Harmonic Oscillators

Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026

Test your understanding with short quizzes. This quiz has 10 questions to check your progress.

Question 1 of 10

A system is undergoing simple harmonic motion (SHM). Which of the following best describes its total mechanical energy at any point in its motion?

All Questions (10)

A system is undergoing simple harmonic motion (SHM). Which of the following best describes its total mechanical energy at any point in its motion?

A) It is the sum of its kinetic and potential energies.

B) It is equal to its maximum kinetic energy only.

C) It is equal to its maximum potential energy only.

D) It is the difference between its kinetic and potential energies.

Correct Answer: A

Based on the provided content, the total energy of a system exhibiting SHM is defined as the sum of the system’s kinetic and potential energies. The relevant equation is E_total = U + K.

For an ideal spring-object system oscillating with simple harmonic motion, which of the following quantities remains constant throughout the motion?

A) Kinetic energy

B) Potential energy

C) Total mechanical energy

D) Velocity of the object

Correct Answer: C

The provided content states that 'Conservation of energy indicates that the total energy of a system exhibiting SHM is constant.' Kinetic and potential energies continuously transform into one another, and the velocity changes, but their sum (total mechanical energy) remains constant.

An object attached to a spring is oscillating in SHM. When the object is at its maximum displacement from the equilibrium position, which statement about its energy is correct?

A) Its kinetic energy is at a maximum, and its potential energy is zero.

B) Its potential energy is at a maximum, and its kinetic energy is zero.

C) Both its kinetic and potential energies are at a maximum.

D) Both its kinetic and potential energies are zero.

Correct Answer: B

At the maximum displacement (the amplitude), the object momentarily stops before changing direction. At this point, its velocity is zero, so its kinetic energy is zero. Since the total energy (E_total = U + K) is constant, if K=0, the potential energy U must be at its maximum value, equal to the total energy.

A spring-object system undergoes simple harmonic motion with amplitude A and total mechanical energy E. If the amplitude of the oscillation is doubled to 2A, what is the new total mechanical energy of the system?

A) E/2

B) E

C) 2E

D) 4E

Correct Answer: D

The total energy of a spring-object system is given by the equation E_total = (1/2)kA^2. Since the energy is proportional to the square of the amplitude (A^2), doubling the amplitude (A → 2A) will cause the total energy to increase by a factor of (2)^2, which is 4. The new energy will be 4E.

According to the provided information for a spring-object system in SHM, changing which of the following properties will directly change the total energy of the system?

A) The mass of the object

B) The period of oscillation

C) The amplitude of the oscillation

D) The frequency of the oscillation

Correct Answer: C

The content explicitly states, 'Changing the amplitude of a system exhibiting SHM will change the maximum potential energy of the system and, therefore, the total energy of the system.' The relevant equation, E_total = (1/2)kA^2, shows a direct relationship between total energy and amplitude.

A mass oscillating on a spring passes through its equilibrium position. At this instant, which of the following is true regarding its energy?

A) The potential energy is maximum.

B) The kinetic energy is maximum.

C) The total mechanical energy is zero.

D) Both kinetic and potential energy are at half their maximum values.

Correct Answer: B

At the equilibrium position, the displacement is zero, so the potential energy stored in the spring is zero. According to the conservation of energy (E_total = U + K), if the potential energy (U) is zero, the kinetic energy (K) must be equal to the total energy, which is its maximum possible value.

A spring-mass system is in simple harmonic motion with total energy E. At a certain point in its oscillation, the kinetic energy (K) is equal to the potential energy (U). What is the value of the potential energy at this point in terms of E?

A) E/4

B) E/2

C) E

D) 2E

Correct Answer: B

The total energy is given by E_total = U + K. The problem states that at a specific point, U = K. We can substitute U for K in the energy equation: E_total = U + U = 2U. Solving for U gives U = E_total / 2. Therefore, at the point where kinetic and potential energies are equal, each is equal to half of the total energy.

For a given spring-object system undergoing SHM, the total mechanical energy is determined by the spring constant (k) and which other quantity?

A) The mass of the object (m)

B) The maximum velocity of the object (v_max)

C) The amplitude of the motion (A)

D) The acceleration due to gravity (g)

Correct Answer: C

The provided equation for the total energy of a spring-object system is E_total = (1/2)kA^2. This equation shows that for a given spring (constant k), the total energy is determined by the amplitude (A).

An object on a spring oscillates in SHM. As the object moves from one of its amplitude positions towards the equilibrium position, how do its kinetic and potential energies change?

A) Kinetic energy increases, and potential energy increases.

B) Kinetic energy decreases, and potential energy increases.

C) Kinetic energy increases, and potential energy decreases.

D) Kinetic energy decreases, and potential energy decreases.

Correct Answer: C

At the amplitude position, potential energy is maximum and kinetic energy is zero. As the object moves towards the equilibrium position, its speed increases, so its kinetic energy increases. Simultaneously, the spring becomes less stretched/compressed, so its potential energy decreases. This is consistent with the conservation of total energy (E_total = U + K), where a decrease in U must be accompanied by an increase in K.

A spring-mass system oscillates with a total energy of 16 J. If an external action reduces the total energy of the system to 4 J without changing the spring or the mass, by what factor has the amplitude of the oscillation changed?

A) It is reduced to 1/4 of its original value.

B) It is reduced to 1/2 of its original value.

C) It is reduced to 1/16 of its original value.

D) It remains unchanged.

Correct Answer: B

The total energy is proportional to the square of the amplitude (E ∝ A^2). Therefore, the amplitude is proportional to the square root of the energy (A ∝ √E). The energy is reduced from 16 J to 4 J, which is a reduction to 4/16 = 1/4 of the original energy. The amplitude will therefore be reduced by a factor of √(1/4) = 1/2.