• 55 questions

AP Physics Simple Harmonic Motion Practice Test

Unofficial multiple-choice practice for Unit 7 of AP Physics 1, Oscillations: springs, pendulums, period and energy.

Which condition makes an oscillation simple harmonic?

Pick an answer, then press Check answer. Then you see Correct or Not quite, with the reason. Keys: A to D pick, Enter checks.

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Unofficial practice questions, not affiliated with the College Board. Bank checked October 11, 2026.

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Topic 7.1: Defining simple harmonic motion 12

  • A 0.20 kg mass hung from a vertical spring stretches it 0.040 m before coming to rest. Taking g = 10 m/s², what is the spring constant? Wikipedia, "Hooke's law" and Wikipedia, "Simple harmonic motion"; course topic 7.1
  • A 0.50 kg block is attached to an ideal spring with k = 50 N/m on a frictionless table. What is the magnitude of the block's acceleration when it is 0.10 m from equilibrium? Wikipedia, "Simple harmonic motion"; course topic 7.1
  • A block on a spring is displaced to the right of its equilibrium position. In which direction does the restoring force act? AP Physics 1 Course and Exam Description, essential knowledge 7.1.A.2.i and Wikipedia, "Restoring force"; course topic 7.1
  • A block on a spring is released from rest at maximum stretch. Why does it not stop when it reaches the equilibrium position? Wikipedia, "Simple harmonic motion"; course topic 7.1
  • A block on an ideal spring feels a 6.0 N restoring force when it is 4.0 cm from equilibrium. What restoring force acts on it at 1.0 cm from equilibrium? Wikipedia, "Simple harmonic motion"; course topic 7.1
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Topic 7.1: Defining simple harmonic motion, continued

  • A block oscillates on an ideal spring. As it moves from maximum displacement toward equilibrium, what happens to the size of the restoring force and to the block's speed? Wikipedia, "Simple harmonic motion"; course topic 7.1
  • A graph shows the force an ideal spring exerts on a block against the block's displacement from equilibrium. What does the graph look like? Wikipedia, "Simple harmonic motion"; course topic 7.1
  • An ideal spring with spring constant 200 N/m is stretched 0.050 m from its relaxed length. What is the magnitude of the force the spring exerts? Wikipedia, "Simple harmonic motion"; course topic 7.1
  • What is true at the equilibrium position of an oscillating system? AP Physics 1 Course and Exam Description, essential knowledge 7.1.A.2.ii and Wikipedia, "Mechanical equilibrium"; course topic 7.1
  • Which condition makes an oscillation simple harmonic? AP Physics 1 Course and Exam Description, essential knowledge 7.1.A.2 and Wikipedia, "Simple harmonic motion"; course topic 7.1
  • Which motion is periodic but not simple harmonic? AP Physics 1 Course and Exam Description, essential knowledge 7.1.A.1 and 7.1.A.2; course topic 7.1
  • Why can the swing of a pendulum be modeled as simple harmonic motion only when the angle is small? AP Physics 1 Course and Exam Description, essential knowledge 7.1.A.2.iii and Wikipedia, "Simple harmonic motion"; course topic 7.1

Topic 7.2: Frequency and period 16

  • A 0.50 kg block on an ideal spring oscillates with a period of 0.50 s. What is the spring constant? Wikipedia, "Simple harmonic motion"; course topic 7.2
  • A 2.0 kg block oscillates on an ideal spring with k = 200 N/m. What is the period of the motion? Wikipedia, "Simple harmonic motion"; course topic 7.2
  • A block on a spring oscillates at 2.0 Hz. With the same spring, what mass would oscillate at 1.0 Hz? Wikipedia, "Simple harmonic motion"; course topic 7.2
  • A block oscillates on a horizontal ideal spring with period T on Earth. The same block and spring are set up where g is one sixth as large. What is the period there? Wikipedia, "Simple harmonic motion"; course topic 7.2
  • A mass on a spring completes 20 full oscillations in 8.0 s. What is its period? Wikipedia, "Frequency"; course topic 7.2
  • A pendulum clock runs slow. Which change to the pendulum would shorten its period? Wikipedia, "Pendulum"; course topic 7.2
  • A pendulum has a period of 2.0 s. It is shortened to one quarter of its length. What is the new period? Wikipedia, "Pendulum"; course topic 7.2
  • A pendulum is carried to a place where g is one sixth of its value on Earth. By about what factor does its period change? Wikipedia, "Pendulum"; course topic 7.2
  • A simple pendulum is 1.0 m long and swings through a small angle where g = 9.8 m/s². What is its period, to two figures? Wikipedia, "Pendulum" and Wikipedia, "Seconds pendulum"; course topic 7.2
  • A spring is swapped for one four times as stiff, and the same block is attached. How does the period of oscillation change? Wikipedia, "Simple harmonic motion"; course topic 7.2
  • An oscillator has a period of 0.25 s. What is its frequency? AP Physics 1 Course and Exam Description, essential knowledge 7.2.A.1 and Wikipedia, "Frequency"; course topic 7.2
  • The bob of a simple pendulum is replaced by one with twice the mass, and the length is kept the same. What happens to the period? Wikipedia, "Pendulum"; course topic 7.2
  • The mass on an ideal spring is replaced by one four times as large. How does the period change? Wikipedia, "Simple harmonic motion"; course topic 7.2
  • Students hang different masses m from one spring, measure the period T for each, and plot T² against m. The points fall on a straight line of slope 0.40 s²/kg. What is the spring constant? Wikipedia, "Simple harmonic motion"; course topic 7.2
  • Students time a pendulum at several lengths L and plot T² against L. The line of best fit has slope 4.0 s²/m. What value of g does the experiment give? Wikipedia, "Pendulum"; course topic 7.2
  • Two pendulums swing through small angles side by side. Pendulum X is 0.25 m long and pendulum Y is 1.0 m long. How do their frequencies compare? Wikipedia, "Pendulum"; course topic 7.2

Topic 7.3: Representing and analyzing SHM 13

  • A block on a spring is pulled back twice as far as before and released. How does the period compare with the first trial? AP Physics 1 Course and Exam Description, essential knowledge 7.3.A.2 and Wikipedia, "Simple harmonic motion"; course topic 7.3
  • A block on a spring is released from rest at x = +A. Which describes the graph of its velocity against time over the first full period? AP Physics 1 Course and Exam Description, essential knowledge 7.3.A.3 and Wikipedia, "Simple harmonic motion"; course topic 7.3
  • A position–time graph of an oscillator swings between +0.10 m and −0.10 m, and neighboring peaks are 0.80 s apart. What are the amplitude and the frequency? Wikipedia, "Simple harmonic motion" and AP Physics 1 Course and Exam Description, essential knowledge 7.3.A.3; course topic 7.3
  • The amplitude of a block–spring oscillator is doubled, with the same block and spring. What happens to the block's maximum speed? Wikipedia, "Simple harmonic motion"; course topic 7.3
  • An object in SHM with period T is released from rest at x = +A at time t = 0. Where is it at t = T/4, and which way is it moving? AP Physics 1 Course and Exam Description, essential knowledge 7.3.A.1.ii; course topic 7.3
  • An oscillator has amplitude 0.10 m and frequency 2.0 Hz. What is its maximum speed? Wikipedia, "Simple harmonic motion"; course topic 7.3
  • An oscillator has an amplitude of 0.050 m. What total distance does it travel in one full period? Wikipedia, "Simple harmonic motion"; course topic 7.3
  • An oscillator's position in meters is x = 0.20 cos(4πt), with t in seconds. What is its period? AP Physics 1 Course and Exam Description, essential knowledge 7.3.A.1; course topic 7.3
  • At an instant when an oscillator's velocity is zero, which statement is correct? AP Physics 1 Course and Exam Description, essential knowledge 7.3.A.1.i and Wikipedia, "Simple harmonic motion"; course topic 7.3
  • At which point in its cycle does an object in simple harmonic motion have its greatest speed? Wikipedia, "Simple harmonic motion"; course topic 7.3
  • At which point in its cycle is the magnitude of an oscillator's acceleration greatest? Wikipedia, "Simple harmonic motion"; course topic 7.3
  • The position of an oscillator is x = A cos(2πft). Where is the object at t = 0, and how is it moving? AP Physics 1 Course and Exam Description, essential knowledge 7.3.A.1 and Wikipedia, "Simple harmonic motion"; course topic 7.3
  • While an oscillating block is at a positive displacement and moving back toward equilibrium, what are the signs of its velocity and acceleration? Wikipedia, "Simple harmonic motion"; course topic 7.3

Topic 7.4: Energy of simple harmonic oscillators 14

  • A 0.20 kg pendulum bob is released from rest 0.050 m above the lowest point of its swing. Taking g = 10 m/s², how fast is it moving at the lowest point? AP Physics 1 Course and Exam Description, essential knowledge 7.4.A.2; course topic 7.4
  • A 0.50 kg block on an ideal spring with k = 200 N/m oscillates with amplitude 0.10 m. What is its speed as it passes through equilibrium? Wikipedia, "Simple harmonic motion"; course topic 7.4
  • A 2.0 kg block on an ideal spring with k = 50 N/m passes through equilibrium at 0.50 m/s. What is the amplitude of its motion? Wikipedia, "Simple harmonic motion"; course topic 7.4
  • A block on an ideal spring with k = 100 N/m oscillates with an amplitude of 0.20 m. What is the total mechanical energy of the system? Wikipedia, "Simple harmonic motion" and AP Physics 1 Course and Exam Description, essential knowledge 7.4.A.4.ii; course topic 7.4
  • A block–spring oscillator has amplitude A. When the block is at x = A/2, what fraction of the system's energy is kinetic? Wikipedia, "Simple harmonic motion"; course topic 7.4
  • A block–spring oscillator with k = 100 N/m has 0.50 J of total energy. What is the block's kinetic energy when it is 0.060 m from equilibrium? Wikipedia, "Simple harmonic motion"; course topic 7.4
  • A graph shows the total mechanical energy of a frictionless block–spring oscillator against time. What does it look like? AP Physics 1 Course and Exam Description, essential knowledge 7.4.A.2 and Wikipedia, "Simple harmonic motion"; course topic 7.4
  • The amplitude of a block–spring oscillator is doubled. By what factor does the total energy of the system change? AP Physics 1 Course and Exam Description, essential knowledge 7.4.A.4.ii and Wikipedia, "Simple harmonic motion"; course topic 7.4
  • An ideal oscillator has 8.0 J of total mechanical energy. At one instant its potential energy is 3.0 J. What is its kinetic energy at that instant? AP Physics 1 Course and Exam Description, essential knowledge 7.4.A.1; course topic 7.4
  • At what displacement does a block–spring oscillator of amplitude A have equal kinetic and potential energy? Wikipedia, "Simple harmonic motion"; course topic 7.4
  • How many times during one full period does the kinetic energy of an oscillator reach its maximum? AP Physics 1 Course and Exam Description, essential knowledge 7.4.A.3 and Wikipedia, "Simple harmonic motion"; course topic 7.4
  • Two identical blocks oscillate on identical springs. Block X has amplitude A and block Y has amplitude 3A. How do the total energies compare? Wikipedia, "Simple harmonic motion"; course topic 7.4
  • What is the kinetic energy of an oscillating block at the instant it reaches maximum displacement? AP Physics 1 Course and Exam Description, essential knowledge 7.4.A.4 and 7.4.A.4.i; course topic 7.4
  • Where is the kinetic energy of a block–spring oscillator greatest? AP Physics 1 Course and Exam Description, essential knowledge 7.4.A.3; course topic 7.4

How this list was compiled: Our own questions, written to Unit 7 (Oscillations) of the College Board's AP Physics 1: Algebra-Based Course and Exam Description, effective fall 2024, https://apcentral.collegeboard.org/media/pdf/ap-physics-1-course-and-exam-description.pdf, read 2026-10-11. Every numeric answer is worked from the numbers the question prints and was worked out a second time on 2026-10-11. The principle behind each answer was read on 2026-10-11 in the Wikipedia article or the essential knowledge statement of the course description named under the question. Licence: Own work. Short quotations from the public documents named under each question.

How it works

This AP Physics simple harmonic motion practice test has 55 questions of our own on Unit 7 of AP Physics 1, Oscillations. It is unofficial and not affiliated with or endorsed by the College Board, the owner of AP.

Read the full guide

What Unit 7 covers

The College Board's course description, read October 11, 2026, gives Unit 7 four topics and no weights among them, so the spread is ours: defining simple harmonic motion (12 questions), frequency and period (16), representing and analyzing the motion (13), and the energy of simple harmonic oscillators (14).

Solutions and sources

Every numeric answer is worked from the numbers the question prints and was worked out a second time as a check. Under each answer is the Wikipedia article or the line of the course description where the principle can be read.

  • At the turning points speed is zero and acceleration is greatest. At equilibrium it is the reverse.
  • Energy goes with the square of the amplitude: double the amplitude and the total energy is four times as large.

Questions and answers

What unit is simple harmonic motion in AP Physics 1?

Unit 7, Oscillations, the seventh of eight units. It carries 5 to 8% of the multiple-choice section, by the College Board's course page.

Is there an AP Physics 1 waves and simple harmonic motion practice test?

This page is the simple harmonic motion part. Waves are not among the eight units of AP Physics 1 today; the College Board lists Waves, Sound, and Physical Optics as Unit 14 of AP Physics 2.

What are the period formulas for a spring and a pendulum?

For a block on an ideal spring, T = 2π√(m/k). For a simple pendulum at small angles, T = 2π√(L/g). Neither depends on amplitude, and the pendulum's does not depend on the bob's mass.

Does this AP Physics practice test on oscillations fit AP Physics C?

In part. Unit 7 of AP Physics C: Mechanics is also named Oscillations, at 10 to 15% of its multiple-choice section, but that course is calculus-based. These questions follow AP Physics 1 and use algebra only.

Are these real AP Physics 1 exam questions?

No. The College Board owns the real questions, and none appears here, even in other words. Every question was written for this page from the topics the course description lists.

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