---
title: "AP Physics 1 Unit 7 Practice Test"
description: "A timed AP Physics 1 Unit 7 (Oscillations) practice test in the AP format, drawn from 645 multiple-choice questions and 44 FRQs written for the unit. The standard version takes about 88 minutes."
canonical: "https://fiveable.me/ap-physics-1-revised/unit-test/7"
type: "unit-test"
subject: "AP Physics 1"
unit: "Unit 7"
---

# AP Physics 1 Unit 7 Practice Test

## Overview

A timed AP Physics 1 Unit 7 (Oscillations) practice test in the AP format, drawn from 645 multiple-choice questions and 44 FRQs written for the unit. The standard version takes about 88 minutes.

## Test Format

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

## Unit FRQs by Type

- [FRQ 1 – Mathematical Routines](/ap-physics-1-revised/frqs/mathematical-routines?unit=7): 9 questions
- [FRQ 2 – Translation Between Representations](/ap-physics-1-revised/frqs/translation-between-representations?unit=7): 6 questions
- [FRQ 3 – Experimental Design](/ap-physics-1-revised/frqs/experimental-design?unit=7): 10 questions
- [FRQ 4 – Qualitative/Quantitative Translation](/ap-physics-1-revised/frqs/qualitative-quantitative-translation?unit=7): 19 questions

## Practice Questions

### Question 1

A mass attached to a spring oscillates with amplitude $$A$$. The average speed of the mass over one period is $$s_{avg}$$. If the amplitude is increased to $$2A$$ while the period remains constant, what is the new average speed?

- (A) $$2s_{avg}$$
- (B) $$4s_{avg}$$
- (C) $$s_{avg}$$
- (D) $$0.5s_{avg}$$

**Answer: (A)** Average speed is total distance divided by time ($$4A/T$$). Since $$T$$ is constant, average speed is directly proportional to amplitude $$A$$.

### Question 2

A pendulum of length $$L$$ has a period $$T$$ on a planet with surface gravity $$g$$. If the pendulum is moved to a planet with the same radius but twice the density, which expression gives the new period?

- (A) $$2\pi\sqrt{\frac{L}{2g}}$$
- (B) $$2\pi\sqrt{\frac{2L}{g}}$$
- (C) $$2\pi\sqrt{\frac{L}{g}}$$
- (D) $$2\pi\sqrt{\frac{L}{4g}}$$

**Answer: (A)** Gravity $$g$$ is proportional to density $$\rho$$ for constant radius ($$g \propto M \propto \rho$$). Doubling density doubles $$g$$. The new period is $$2\pi\sqrt{L/(2g)}$$.

### Question 3

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?

- (A) $$0.67 T$$
- (B) $$1.5 T$$
- (C) $$2.25 T$$
- (D) $$3.0 T$$

**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 4

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?

- (A) $$0.25 T$$
- (B) $$0.50 T$$
- (C) $$2.0 T$$
- (D) $$4.0 T$$

**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 5

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?

- (A) System 1 has a larger spring constant and a shorter period
- (B) System 1 has a larger spring constant and a longer period
- (C) System 1 has a smaller spring constant and a shorter period
- (D) System 1 has a smaller spring constant and a longer period

**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 6

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?

- (A) $$T/16$$
- (B) $$T/4$$
- (C) $$T$$
- (D) $$4T$$

**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 7

A block of mass $$m$$ attached to a spring oscillates with amplitude $$A$$ and maximum speed $$v_{max}$$. If the block is replaced by one with mass $$4m$$ while keeping the amplitude $$A$$ constant, what is the new maximum speed?

- (A) The new maximum speed is $$v_{max}/2$$
- (B) The new maximum speed is $$v_{max}/4$$
- (C) The new maximum speed is $$2v_{max}$$
- (D) The new maximum speed is $$4v_{max}$$

**Answer: (A)** Equating maximum potential energy $$\frac{1}{2}kA^2$$ to maximum kinetic energy $$\frac{1}{2}mv_{max}^2$$ yields $$v_{max} = A\sqrt{k/m}$$. Since speed is inversely proportional to the square root of mass ($$v_{max} \propto 1/\sqrt{m}$$), quadrupling the mass reduces speed by a factor of $$\sqrt{4} = 2$$.

### Question 8

A block of mass $$m$$ on a frictionless surface is attached to a spring with constant $$k$$. The system oscillates with maximum speed $$v_0$$. If the mass is replaced with $$4m$$ while keeping the amplitude constant, what is the new maximum speed?

- (A) $$v_0/2$$, because maximum speed is inversely proportional to the square root of the mass.
- (B) $$v_0/4$$, because maximum speed is inversely proportional to the mass of the block.
- (C) $$2v_0$$, because maximum speed is directly proportional to the square root of the mass.
- (D) $$4v_0$$, because maximum speed is directly proportional to the mass of the block.

**Answer: (A)** Equating maximum potential energy ($$\frac{1}{2}kA^2$$) to maximum kinetic energy ($$\frac{1}{2}mv^2$$) shows that $$v$$ is proportional to $$1/\sqrt{m}$$.

### Question 9

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 $$g$$?

- (A) $$2\pi\sqrt{\frac{d}{g}}$$
- (B) $$2\pi\sqrt{\frac{g}{d}}$$
- (C) $$\frac{1}{2\pi}\sqrt{\frac{d}{g}}$$
- (D) $$\frac{1}{2\pi}\sqrt{\frac{g}{d}}$$

**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 10

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) $$A\sqrt{\frac{k}{m}}$$
- (B) $$A\sqrt{\frac{m}{k}}$$
- (C) $$A^2\sqrt{\frac{k}{m}}$$
- (D) $$A^2\sqrt{\frac{m}{k}}$$

**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 $$A\sqrt{k/m}$$.

## Review the Unit

- [7.1 Defining Simple Harmonic Motion (SHM)](/ap-physics-1-revised/unit-7/1-defining-simple-harmonic-motion-shm/study-guide/GMUA9ME65plxVw8X)
- [7.2 Frequency and Period of SHM](/ap-physics-1-revised/unit-7/2-frequency-and-period-of-shm/study-guide/Od6DWgUt5QKX7MS7)
- [7.3 Representing and Analyzing SHM](/ap-physics-1-revised/unit-7/3-representing-and-analyzing-shm/study-guide/NbpEFEgkYT1oVUfE)
- [7.4 Energy of Simple Harmonic Oscillators](/ap-physics-1-revised/unit-7/4-energy-of-simple-harmonic-oscillators/study-guide/iNk88ABPvO1dza7N)

## Other Unit Tests

- [Unit 1: Kinematics](/ap-physics-1-revised/unit-test/1)
- [Unit 2: Force and Translational Dynamics](/ap-physics-1-revised/unit-test/2)
- [Unit 3: Work, Energy, and Power](/ap-physics-1-revised/unit-test/3)
- [Unit 4: Linear Momentum](/ap-physics-1-revised/unit-test/4)
- [Unit 5: Torque and Rotational Dynamics](/ap-physics-1-revised/unit-test/5)
- [Unit 6: Rotating Systems: Energy & Momentum](/ap-physics-1-revised/unit-test/6)
- [Unit 8: Fluids](/ap-physics-1-revised/unit-test/8)

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