AP Physics 1: Algebra-Based, AP exams, 5–8%

Unit 7: Oscillations

Unit 7 covers simple harmonic motion in mass-spring and pendulum systems. Period and frequency, the shape of the position, velocity, and acceleration curves, and the energy exchange between kinetic and potential forms are the core ideas. The exam frequently asks what changes the period and what does not.

Position: 7 of 8 units
Published weighting: 5–8% in the official framework
Topics covered: 4 topics in this guide

What is covered

Topics inside this unit.

These topics describe the scope students most often review for this part of AP Physics 1: Algebra-Based. Treat them as a study checklist rather than an exhaustive list of what a single exam form can sample.

Defining simple harmonic motion: The restoring force proportional to displacement, and which systems satisfy that condition.
Frequency and period: Period of a mass-spring system and a simple pendulum, and which variables each depends on.
Representing and analyzing oscillations: Amplitude, phase, and the relative timing of position, velocity, and acceleration curves.
Energy of simple harmonic oscillators: Continuous exchange between kinetic and elastic or gravitational potential energy over one cycle.

Study tips

How to practice Oscillations.

Section-specific guidance that follows from how this material is usually tested.

Memorize which variables do and do not affect period for both systems; that contrast is heavily tested.
Sketch position, velocity, and acceleration on shared axes to fix the phase relationships.
Identify the equilibrium position first in every oscillation problem; it anchors the whole analysis.

Where this fits

Unit 7: Oscillations is 7 of 8 units in the AP Physics 1: Algebra-Based guide, and it carries a published weighting of 5–8% in the official framework. Use the full guide to balance it against everything else you have to review.

Back to the AP Physics 1: Algebra-Based guide Official exam information

Sample Oscillations questions

Practice questions, not yet expert-reviewed

Original practice questions written to the published framework for this section. No expert has reviewed them, and they are not taken from any official exam. Try each one before you open the answer.

Question 1Foundational
A 0.50 kg block attached to an ideal spring of spring constant 200 N/m oscillates on a frictionless horizontal surface. What is the period of the oscillation?
1. A0.16 s
2. B0.31 s
3. C0.63 s
4. D3.1 s
Show answer
Answer: B. 0.31 s
The period is T = 2(pi)sqrt(m/k) = 2(pi)sqrt(0.50/200) = 2(pi)(0.050) = 0.31 s. The 3.1 s choice comes from a decimal slip that reads sqrt(0.0025) as 0.50 rather than 0.050, and 0.63 s doubles the result by using 4(pi).
Key insight: A stiffer spring or a lighter block shortens the period, and the amplitude has no effect at all.
Question 2Foundational
A simple pendulum swinging with small amplitude has a period of 2.0 s. If its length is made four times as long and it stays at the same location, what is its new period?
1. A1.0 s
2. B2.8 s
3. C4.0 s
4. D8.0 s
Show answer
Answer: C. 4.0 s
Because T = 2(pi)sqrt(L/g), the period scales with the square root of the length, so quadrupling L doubles T from 2.0 s to 4.0 s. The 8.0 s choice scales the period directly with length instead of with its square root.
Key insight: Pendulum period depends on length and g only, so the mass of the bob and the (small) amplitude do not matter.
Question 3Intermediate
True or false: doubling the amplitude of an ideal mass-spring oscillator, with the same block and the same spring, leaves the period of the oscillation unchanged.
1. ATrue
2. BFalse
Show answer
Answer: A. True
For an ideal spring the restoring force is proportional to displacement, and the period T = 2(pi)sqrt(m/k) contains no amplitude term. A larger amplitude means the block travels farther but also moves proportionally faster, so the round trip takes the same time.
Key insight: Amplitude independence is the defining signature of simple harmonic motion.
Question 4Intermediate
A 0.20 kg block on a frictionless surface oscillates on a spring of spring constant 80 N/m with an amplitude of 0.10 m. What is the maximum speed of the block?
1. A0.20 m/s
2. B1.0 m/s
3. C2.0 m/s
4. D4.0 m/s
Show answer
Answer: C. 2.0 m/s
All of the energy (1/2)kA^2 = (1/2)(80)(0.10)^2 = 0.40 J becomes kinetic energy at the equilibrium point, so (1/2)(0.20)v^2 = 0.40 J and v = 2.0 m/s. The same result follows from v(max) = (omega)A with omega = sqrt(80/0.20) = 20 rad/s.
Key insight: The oscillator is fastest at equilibrium, where the potential energy is zero and all the energy is kinetic.
Question 5Advanced
A block oscillates on an ideal spring with amplitude A. At what displacement from equilibrium is the block's kinetic energy exactly equal to the elastic potential energy stored in the spring?
1. A0.25A
2. B0.50A
3. C0.71A
4. D0.87A
Show answer
Answer: C. 0.71A
The total energy is (1/2)kA^2, so equal shares means (1/2)kx^2 = (1/2)[(1/2)kA^2], giving x^2 = A^2/2 and x = A/sqrt(2), about 0.71A. The 0.50A choice assumes energy splits evenly at half the amplitude, but energy depends on x squared, not on x.
Key insight: Because energy goes as the square of displacement, the halfway point in energy is not the halfway point in position.

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Unit 7: Oscillations