PrepGo

AP Physics C: Mechanics Practice Quiz: Defining Simple Harmonic Motion (SHM)

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

Test your understanding with short quizzes. This quiz has 7 questions to check your progress.

Question 1 of 7

What is the fundamental condition required for an object's motion to be classified as simple harmonic motion (SHM)?

All Questions (7)

What is the fundamental condition required for an object's motion to be classified as simple harmonic motion (SHM)?

A) The object must move with a constant velocity.

B) The net restoring force on the object must be proportional to its displacement from equilibrium.

C) The net force on the object must always be zero.

D) The object's displacement must be proportional to time.

Correct Answer: B

The provided content explicitly states that simple harmonic motion results when the magnitude of the restoring force exerted on an object is proportional to that object’s displacement from its equilibrium position.

In the equation for simple harmonic motion, $\vec{F}_{net}=-k\Delta\vec{x}$, what is the significance of the negative sign?

A) It indicates that the spring constant, k, is always a negative value.

B) It signifies that the force is always directed in the negative direction on a coordinate axis.

C) It shows that the restoring force vector is always directed opposite to the displacement vector.

D) It implies that the total energy of the system is decreasing.

Correct Answer: C

The negative sign in the equation indicates that the restoring force is a vector that always points in the direction opposite to the displacement vector. If the object is displaced to the right of equilibrium, the force is to the left.

An object is undergoing SHM. At which point in its motion is the magnitude of the net restoring force at its maximum?

A) At the equilibrium position.

B) At the point of maximum displacement.

C) When the object's speed is greatest.

D) The restoring force is constant throughout the motion.

Correct Answer: B

According to the equation $\vec{F}_{net}=-k\Delta\vec{x}$, the magnitude of the force is directly proportional to the magnitude of the displacement ($\Delta\vec{x}$). Therefore, the force is greatest when the displacement is greatest.

What is the net restoring force on an object in simple harmonic motion as it passes through its equilibrium position?

A) Zero

B) Equal to k

C) Its maximum positive value

D) Its maximum negative value

Correct Answer: A

The equilibrium position is defined as the point where the displacement ($\Delta\vec{x}$) is zero. Substituting $\Delta\vec{x} = 0$ into the equation $\vec{F}_{net}=-k\Delta\vec{x}$ results in a net force of zero.

An object attached to a spring oscillates in simple harmonic motion. If the object's displacement from equilibrium is doubled, how does the magnitude of the restoring force exerted by the spring change?

A) It is quadrupled.

B) It is doubled.

C) It remains the same.

D) It is halved.

Correct Answer: B

The relationship $\vec{F}_{net}=-k\Delta\vec{x}$ shows a direct, linear proportionality between the magnitude of the force and the magnitude of the displacement. If the displacement is doubled, the magnitude of the restoring force must also double.

The force responsible for simple harmonic motion is called a 'restoring force' because it always acts to...

A) increase the object's displacement from equilibrium.

B) maintain a constant acceleration.

C) push or pull the object back toward its equilibrium position.

D) oppose the motion of the object, regardless of position.

Correct Answer: C

The term 'restoring' implies that the force's purpose is to restore the system to equilibrium. It achieves this by always being directed toward the equilibrium point, opposite the direction of displacement.

Which of the following graphs best represents the relationship between the magnitude of the net restoring force, F, and the magnitude of the displacement, x, for an object in simple harmonic motion?

A) A horizontal line, indicating F is constant.

B) A straight line with a positive slope passing through the origin.

C) A parabola opening upwards, symmetric about the F-axis.

D) A curve that decreases as x increases.

Correct Answer: B

The equation $\vec{F}_{net}=-k\Delta\vec{x}$ describes a linear relationship between the force and displacement vectors. When considering only their magnitudes, F = kx. This is the equation of a straight line with a positive slope (k) that passes through the origin (0,0).