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AP Physics 1: Algebra-Based Practice Quiz: Representing and Analyzing SHM

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

An object is undergoing simple harmonic motion (SHM). At which point in its motion is the object's speed at its maximum?

All Questions (10)

An object is undergoing simple harmonic motion (SHM). At which point in its motion is the object's speed at its maximum?

A) At the point of maximum displacement

B) At the equilibrium position

C) At the halfway point between equilibrium and maximum displacement

D) The speed is constant throughout the motion

Correct Answer: B

In SHM, the velocity is maximum when the object passes through the equilibrium position (where displacement is zero), and the velocity is zero at the points of maximum displacement (the endpoints of the motion).

The displacement of a block attached to a spring is described by the equation x = (0.10 m)cos(2π(5 Hz)t). What does the value 0.10 m represent?

A) The period of the oscillation

B) The frequency of the oscillation

C) The amplitude of the oscillation

D) The equilibrium position of the block

Correct Answer: C

The general equation for displacement in SHM is x = Acos(2πft), where 'A' represents the amplitude, which is the maximum displacement from the equilibrium position. In the given equation, A = 0.10 m.

A pendulum is swinging back and forth with simple harmonic motion. If the amplitude of the swing is doubled, how does the period of the pendulum change?

A) The period is halved.

B) The period is doubled.

C) The period is quadrupled.

D) The period remains unchanged.

Correct Answer: D

A key property of simple harmonic motion is that the period is independent of the amplitude. Therefore, changing the amplitude will not affect the period of the system.

The graph shows the displacement of an object in SHM as a function of time. At which of the labeled points is the magnitude of the object's acceleration the greatest?

A) Point P

B) Point Q

C) Point R

D) Point S

Correct Answer: B

In SHM, acceleration is directly proportional to the displacement from equilibrium and in the opposite direction (a ∝ -x). Therefore, the magnitude of the acceleration is greatest when the magnitude of the displacement is greatest. On the graph, Point Q represents the maximum displacement (amplitude).

An object executing simple harmonic motion is momentarily at rest. At that instant, what can be said about its displacement and the magnitude of its acceleration?

A) Displacement is zero, and acceleration is zero.

B) Displacement is maximum, and acceleration is zero.

C) Displacement is zero, and acceleration is maximum.

D) Displacement is maximum, and acceleration is maximum.

Correct Answer: D

An object in SHM is momentarily at rest at its endpoints, which are the points of maximum displacement (amplitude). At these points, the restoring force is greatest, and therefore the magnitude of the acceleration (a ∝ -x) is also at its maximum.

The motion of a particle is described by x = A sin(2πft). At time t=0, what is the initial displacement of the particle?

A) A

B) A/2

C) 0

D) -A

Correct Answer: C

To find the displacement at t=0, substitute t=0 into the equation: x = A sin(2πf * 0) = A sin(0). Since sin(0) = 0, the initial displacement x is 0. This means the particle starts at the equilibrium position.

The displacement of an object in SHM is shown in the graph as a solid line. Which of the dashed lines best represents the velocity of the object as a function of time?

A) A cosine curve (starts at max, goes to zero)

B) A negative sine curve (starts at zero, goes negative)

C) A negative cosine curve (starts at min, goes to zero)

D) A sine curve shifted by a quarter period (same as the displacement curve)

Correct Answer: A

Velocity is the rate of change (slope) of displacement. The given displacement graph is a sine curve, which starts at the origin with a maximum positive slope. The velocity graph must therefore start at its maximum positive value. A cosine curve starts at its maximum value, correctly representing the velocity.

A mass on a spring oscillates with a period T and an amplitude A. The mass is stopped and then set into oscillation again with an amplitude of A/2. What is the new period of oscillation?

A) 2T

B) T

C) T/2

D) T/4

Correct Answer: B

According to the principles of SHM, the period of a mass-spring system depends on the mass and the spring constant, but not on the amplitude of the oscillation. Therefore, changing the amplitude does not change the period.

An object's displacement from equilibrium is given by x = A cos(2πft). At what time t is the object first at its maximum negative displacement?

A) t = 1/(4f)

B) t = 1/(2f)

C) t = 3/(4f)

D) t = 1/f

Correct Answer: B

The period T is equal to 1/f. The cosine function starts at its maximum positive value (at t=0). It reaches its maximum negative value (-1) when its argument (2πft) equals π. Solving 2πft = π for t gives t = 1/(2f). This corresponds to half a period, t = T/2.

For an object in simple harmonic motion, which of the following quantities is greatest in magnitude when the object's kinetic energy is zero?

A) Velocity

B) Displacement

C) Momentum

D) Kinetic Energy

Correct Answer: B

An object's kinetic energy is zero when its velocity is zero. In SHM, the velocity is zero at the endpoints of the motion, which are the points of maximum displacement from equilibrium. At these same points, the acceleration is also at its maximum magnitude, but displacement is the quantity listed that is at its maximum.