A block of mass $$m$$ is attached to two identical springs with spring constant $$k$$. In System 1, the springs are arranged in parallel. In System 2, the springs are arranged in series. How do the effective spring constant and the period of oscillation compare between System 1 and System 2?

System 1 has a larger spring constant and a shorter period

System 1 has a larger spring constant and a longer period

System 1 has a smaller spring constant and a shorter period

System 1 has a smaller spring constant and a longer period

A block of mass $$m$$ is attached to a vertical spring with spring constant $$k$$. When the block is at its equilibrium position, the spring is stretched by a distance $$d$$ from its natural length. Which of the following expressions gives the period $$T$$ of oscillation for this system in terms of $$d$$ and the acceleration due to gravity $$g$$?

$$\frac{1}{2\pi}\sqrt{\frac{d}{g}}$$

$$\frac{1}{2\pi}\sqrt{\frac{g}{d}}$$

AP Physics 1 Unit 7 Practice Test

Pick a unit and take a timed, AP^®-style test built only from that unit's questions — with AI feedback on every free-response answer.

unit 1 unit 2 unit 3 unit 4 unit 5 unit 6 unit 7 unit 8

Oscillations

Choose your test format

Two ways to practice unit 7

standard

The exam experience, sized to one unit — timed like the real thing

20 Multiple Choice Questions

40 min

1 FRQ – FRQ 1 – Mathematical Routines

24 min

1 FRQ – FRQ 2 – Translation Between Representations

24 min

Sections run back-to-back with the same directions, timers, and scoring as the real exam

Total: 1 hr 28 min

customizable

Pick your own mix of question types

multiple choice questions

free response questions (choose as many as you want)

FRQ 1 – Mathematical Routines · 24 minFRQ 2 – Translation Between Representations · 24 minFRQ 3 – Experimental Design · 24 minFRQ 4 – Qualitative/Quantitative Translation · 24 min

Total: 40 min

How scoring works: multiple choice is scored instantly, free-response answers get point-by-point AI feedback, and your result is a percentage for this unit — not a projected AP^® score.

Ready for the real thing?

take a full-length practice exam

AP Physics 1 Unit 7 practice questions

Try 10 multiple-choice questions from Unit 7 here. Pick an answer to see why it's right or wrong, then take the timed test above for a full AP-style set.

Question 1
A block of mass $m$ attached to a spring with spring constant $k$ oscillates with period $T$ . If the mass is replaced by a block of mass $9m$ and the spring is replaced by one with spring constant $4k$ , which expression represents the new period of the system?
$0.67 T$
$1.5 T$
$2.25 T$
$3.0 T$
Show answer
Answer: (B)
Period $T$ is proportional to $\sqrt{m/k}$ . The factor of change is $\sqrt{9/4} = 3/2 = 1.5$ . The new period is $1.5T$ .
Question 2
A simple pendulum of length $L$ has a period $T$ on Earth. If the pendulum is moved to a planet where the gravitational acceleration is $4g$ , which expression represents the new period of the pendulum?
$0.25 T$
$0.50 T$
$2.0 T$
$4.0 T$
Show answer
Answer: (B)
Period is inversely proportional to the square root of gravity ( $T \propto 1/\sqrt{g}$ ). The factor is $1/\sqrt{4} = 0.5$ . The new period is $0.5T$ .
Question 3
A block of mass $m$ is attached to two identical springs with spring constant $k$ . In System 1, the springs are arranged in parallel. In System 2, the springs are arranged in series. How do the effective spring constant and the period of oscillation compare between System 1 and System 2?
System 1 has a larger spring constant and a shorter period
System 1 has a larger spring constant and a longer period
System 1 has a smaller spring constant and a shorter period
System 1 has a smaller spring constant and a longer period
Show answer
Answer: (A)
Parallel springs add constants ( $k_{eff} = 2k$ ), while series springs add reciprocals ( $k_{eff} = k/2$ ). Since period $T = 2\pi\sqrt{m/k_{eff}}$ , a larger $k_{eff}$ in System 1 results in a shorter period.
Question 4
An object of mass $m$ attached to an ideal spring with spring constant $k$ oscillates with a period $T$ . If the spring is replaced by one with constant $4k$ and the object is replaced by one with mass $m/4$ , what is the new period of oscillation?
$T/16$
$T/4$
$T$
$4T$
Show answer
Answer: (B)
Using $T = 2\pi\sqrt{\frac{m}{k}}$ , the factor of change is $\sqrt{\frac{1/4}{4}} = \sqrt{\frac{1}{16}} = \frac{1}{4}$ .
Question 5
A block of mass $m$ is attached to a vertical spring with spring constant $k$ . When the block is at its equilibrium position, the spring is stretched by a distance $d$ from its natural length. Which of the following expressions gives the period $T$ of oscillation for this system in terms of $d$ and the acceleration due to gravity $g$ ?
$2\pi\sqrt{\frac{d}{g}}$
$2\pi\sqrt{\frac{g}{d}}$
$\frac{1}{2\pi}\sqrt{\frac{d}{g}}$
$\frac{1}{2\pi}\sqrt{\frac{g}{d}}$
Show answer
Answer: (A)
At equilibrium, the spring force balances the weight ( $kd = mg$ ), so the ratio $m/k$ equals $d/g$ . Substituting this into the standard period equation $T = 2\pi\sqrt{m/k}$ yields $T = 2\pi\sqrt{d/g}$ .
Question 6
A particle of mass $m$ undergoes simple harmonic motion with amplitude $A$ attached to a spring of spring constant $k$ . Which of the following expressions correctly gives the maximum speed $v_{max}$ of the particle?
$A\sqrt{\frac{k}{m}}$
$A\sqrt{\frac{m}{k}}$
$A^2\sqrt{\frac{k}{m}}$
$A^2\sqrt{\frac{m}{k}}$
Show answer
Answer: (A)
Conservation of energy equates the maximum potential energy ( $\frac{1}{2}kA^2$ ) to the maximum kinetic energy ( $\frac{1}{2}mv_{max}^2$ ). Solving for $v_{max}$ yields $A\sqrt{k/m}$ .
Question 7
A simple pendulum of length $L$ and mass $m$ is displaced by a small angle $\theta$ from the vertical. Which of the following expressions gives the magnitude of the restoring force $F_{restoring}$ acting on the mass along its arc of motion?
$mg\sin\theta$
$mg\cos\theta$
$mg\tan\theta$
$mg(1-\cos\theta)$
Show answer
Answer: (A)
The restoring force is the component of gravity acting tangent to the arc of motion. Resolving the weight vector $mg$ yields a tangential component of $mg\sin\theta$ directed toward equilibrium.
Question 8
A block of mass $m$ oscillates on a frictionless horizontal surface attached to a spring with spring constant $k$ . If the amplitude of oscillation is $A$ , which expression gives the magnitude of the maximum acceleration $a_{max}$ of the block?
$\frac{kA}{m}$
$\frac{mA}{k}$
$\frac{km}{A}$
$\frac{k}{mA}$
Show answer
Answer: (A)
According to Newton's second law ( $F=ma$ ), the maximum force occurs at maximum displacement ( $F_{max} = kA$ ). Solving for acceleration gives $a_{max} = kA/m$ .
Question 9
A simple pendulum of length $L$ is suspended from the ceiling of an elevator that is accelerating upward with a constant acceleration $a$ . Which of the following expressions gives the period $T$ of the pendulum in this reference frame?
$2\pi\sqrt{\frac{L}{g+a}}$
$2\pi\sqrt{\frac{L}{g-a}}$
$2\pi\sqrt{\frac{L}{a}}$
$2\pi\sqrt{\frac{L}{g}}$
Show answer
Answer: (A)
The effective gravitational field in the accelerating frame is $g_{eff} = g + a$ . Substituting this into the standard pendulum period formula yields $T = 2\pi\sqrt{L/(g+a)}$ .
Question 10
An object of mass $m$ oscillates on a spring with a period $T$ . Which of the following expressions correctly represents the spring constant $k$ in terms of $m$ and $T$ ?
$\frac{4\pi^2 m}{T^2}$
$\frac{2\pi m}{T^2}$
$\frac{m}{4\pi^2 T^2}$
$\frac{4\pi^2 T^2}{m}$
Show answer
Answer: (A)
Starting with the period formula $T = 2\pi\sqrt{m/k}$ , squaring both sides gives $T^2 = 4\pi^2 m/k$ . Rearranging to solve for $k$ yields $k = 4\pi^2 m/T^2$ .

What's on the AP Physics 1 Unit 7 practice test

The standard version takes about 88 minutes and follows the timing and directions of the AP exam, sized to one unit:

20 Multiple Choice Questions (40 minutes)
1 FRQ – FRQ 1 – Mathematical Routines (24 minutes)
1 FRQ – FRQ 2 – Translation Between Representations (24 minutes)

Questions are drawn from 645 multiple-choice questions and 44 FRQs written for Unit 7, Oscillations.

Practice AP Physics 1 Unit 7 FRQs

Answer the unit's free-response questions one at a time and get a score on every part.

FRQ 1 – Mathematical Routines (9 questions)
FRQ 2 – Translation Between Representations (6 questions)
FRQ 3 – Experimental Design (10 questions)
FRQ 4 – Qualitative/Quantitative Translation (19 questions)

AP Physics 1 Unit 7 Practice Test

Choose your test format

standard

customizable

AP Physics 1 Unit 7 practice questions

What's on the AP Physics 1 Unit 7 practice test

Practice AP Physics 1 Unit 7 FRQs

Review Unit 7 before you start

Other AP Physics 1 unit tests

History

Social Science

English & Capstone

Arts

Science

Math & CS

World Languages

Career Kickstart

Study Tools

Company & Help

Teachers, Schools & Parents

AP Exams

Choosing AP Classes

AP Physics 1 Unit 7 Practice Test

Choose your test format

standard

customizable