What do I need to know for AP Physics 1 Topic 7.2?
Topic 7.2 Frequency and Period of SHM: Period is the time for one complete oscillation, while frequency is the number of oscillations per unit time; for ideal SHM they are reciprocals and depend on system parameters, not amplitude in the ideal model.
- Relate period T and frequency f, then compare how spring-mass and small-angle pendulum periods change when mass, spring constant, pendulum length, or gravitational field strength changes.
- Practice target: 42 original MCQs and 4 original FRQs for this exact topic.
- Course alignment: current AP Physics 1 framework for the 2026–27 school year and May 2027 exam.
Frequency and Period of SHM
Period is the time for one complete oscillation, while frequency is the number of oscillations per unit time; for ideal SHM they are reciprocals and depend on system parameters, not amplitude in the ideal model.
Period is the time for one complete oscillation, while frequency is the number of oscillations per unit time; for ideal SHM they are reciprocals and depend on system parameters, not amplitude in the ideal model.
What you need to understand before calculating
Relate period T and frequency f, then compare how spring-mass and small-angle pendulum periods change when mass, spring constant, pendulum length, or gravitational field strength changes.
This page explains the key vocabulary where it is used. Internal links are for deeper study, not a requirement for understanding the sentence you are reading.
Key terms explained on this page
These terms are defined here before they are used in the calculations. A deeper internal link is optional where one exists; the reader does not need to leave this page to understand the current explanation.
Period
Period T is the time for one complete oscillation, measured in seconds.
Real example: If ten cycles take 20 s, the period is 2 s.
Frequency
Frequency f is the number of complete cycles per second, measured in hertz (Hz).
Real example: A 5 Hz oscillator completes five cycles each second.
Translate the physics into a representation
AP Physics 1 frequently asks you to move between words, diagrams, graphs and equations. Use this representation as a reasoning anchor, then explain what each labeled quantity means in this topic.
Core concepts with real physical examples
| Concept | Meaning | Real example 1 | Real example 2 |
|---|---|---|---|
| Period | Time for one full cycle. | A pendulum returning to the same position and direction after 2 s has T=2 s. | Ten cycles in 20 s gives T=2 s. |
| Frequency | Cycles per second in hertz. | A 5 Hz oscillator completes five cycles each second. | If T=0.25 s, f=4 Hz. |
| Reciprocal relationship | Period and frequency describe the same cycle rate in inverse ways: f=1/T and T=1/f. | An oscillator with T=0.20 s has f=5 Hz. | If an oscillator completes fewer cycles each second, its period is longer. |
| Spring-mass dependence | T increases with mass and decreases with spring stiffness. | Adding mass to a spring slows its oscillation. | A stiffer spring oscillates faster with same mass. |
| Pendulum dependence | For small angles, T depends on length and g, not bob mass. | A longer pendulum swings more slowly. | Two bobs of different mass on equal-length pendulums have the same ideal small-angle period. |
Equations and relationships: variables, units, conditions, examples
| Relationship | Variables & SI units | When to use it | Real example |
|---|---|---|---|
| f = 1/T | f: Hz; T: sAll symbols used here: f = frequency (Hz = s⁻¹); T = period (s); m = oscillating mass (kg); k = spring constant (N/m); L = pendulum length (m); g = gravitational acceleration magnitude (m/s²). | Frequency-period reciprocal. | T=.5 s gives f=2 Hz. |
| T_spring = 2π√(m/k) | T: s; m: kg; k: N/mAll symbols used here: f = frequency (Hz = s⁻¹); T = period (s); m = oscillating mass (kg); k = spring constant (N/m); L = pendulum length (m); g = gravitational acceleration magnitude (m/s²). | Ideal mass-spring oscillator. | Larger m gives longer T. |
| T_pendulum = 2π√(L/g) | T: s; L: m; g: m/s²All symbols used here: f = frequency (Hz = s⁻¹); T = period (s); m = oscillating mass (kg); k = spring constant (N/m); L = pendulum length (m); g = gravitational acceleration magnitude (m/s²). | Small-angle simple pendulum. | Longer L gives longer T. |
Worked physical reasoning
Mass added to spring
Situation: Mass doubles with same k.
Physics: Period multiplies by √2, not 2.
Pendulum length
Situation: Length becomes four times larger.
Physics: Period doubles because T∝√L.
Amplitude change
Situation: Ideal spring oscillator amplitude is doubled.
Physics: Ideal period remains unchanged; energy changes, not T.
AP scope and boundary
For the current AP Physics 1 scope, emphasize T and f plus the spring-mass and small-angle pendulum period relationships. The ideal period is independent of amplitude within the model; the pendulum relationship assumes small angular displacement.
Common mistakes—and the corrected physics
| Incorrect idea | Correct understanding |
|---|---|
| Frequency and period increase together. | They are reciprocals. |
| Heavier pendulum bob swings more slowly. | Ideal small-angle pendulum period is independent of bob mass. |
| Doubling spring mass doubles period. | Period changes by square root of mass factor. |
Master this topic beyond a formula list
This checkpoint combines the current AP Physics 1 content boundary with representation, experiment/data reasoning, real situations and cross-topic transfer.
2026–27 mastery checklist
- Define period T and frequency f as reciprocal descriptions of cycle timing.
- Use T = 1/f and compare how spring-mass period depends on m and k.
- Compare how small-angle pendulum period depends on L and g and not on bob mass.
- Use proportional reasoning to predict changes without unnecessary numerical calculation.
Must-not-miss relationship
T_spring = 2π√(m/k), T_pendulum = 2π√(L/g) for the ideal small-angle model, and f = 1/T. Angular frequency ω = 2πf can support representation work but does not replace the required T/f dependencies.
Symbols & SI units used on this topic: f = frequency (Hz = s⁻¹); T = period (s); m = oscillating mass (kg); k = spring constant (N/m); L = pendulum length (m); g = gravitational acceleration magnitude (m/s²).
Two anchor situations
Doubling the spring mass increases period by √2 rather than doubling it.
Changing a pendulum bob’s mass does not change its ideal small-angle period, while increasing length makes the period longer.
Diagram / graph / equation / claim
Create proportionality graphs of T² versus m for a fixed spring and T² versus L for a pendulum; identify what the slope represents.
How to test the physics
Measure periods for several masses on one spring or several pendulum lengths. Linearize with T² and estimate k or g from the best-fit slope.
The pendulum period formula assumes small angular displacement and an idealized point-like bob/string; amplitude independence is an approximation within that regime.
Use period to set the horizontal timescale for x, v and a graphs in Topic 7.3.
Connect to Topic 7.3 SHM representationsGo beyond memorizing the equation
This topic now combines model selection, physical intuition, a worked transfer problem, graph/data analysis, answer verification, and the four current AP free-response reasoning modes.
Choose the model before calculating
Choose the oscillator model—mass–spring or small-angle pendulum—then identify which physical parameters control period and which do not.
Why the physics works
The period emerges from the competition between inertia and the restoring interaction: more mass slows a spring oscillator, stiffer springs speed it up, and longer pendulums take longer to swing.
Solve this before opening the solution
A mass–spring oscillator has m=4.0 kg and k=100 N/m. Find its period.
Reveal complete reasoning
Solution: T=2π√(m/k)=2π√0.04=0.4π≈1.26 s.
Physics check: A stiffer spring would reduce T, while a larger mass would increase T.
What should you plot?
For a spring oscillator, plot T² versus m; for a small-angle pendulum, plot T² versus L.
What does the graph mean?
Slopes are 4π²/k and 4π²/g respectively, turning square-root laws into linear tests.
How this exact topic can appear in each current FRQ mode
T_spring = 2π√(m/k), T_pendulum = 2π√(L/g) for the ideal small-angle model, and f = 1/T. Angular frequency ω = 2πf can support representation work but does not replace the required T/f dependencies.
Create proportionality graphs of T² versus m for a fixed spring and T² versus L for a pendulum; identify what the slope represents.
Measure periods for several masses on one spring or several pendulum lengths. Linearize with T² and estimate k or g from the best-fit slope.
Use period to set the horizontal timescale for x, v and a graphs in Topic 7.3.
State the oscillator type and model conditions, especially the small-angle condition for a pendulum, before applying a period relation.
Continue with the exact topic question banks
Use the focused banks for skill practice. The five full model papers are reserved for whole-exam simulation.
Topic 7.2 quick review
What is the definition I should know first?
Period is the time for one complete oscillation, while frequency is the number of oscillations per unit time; for ideal SHM they are reciprocals and depend on system parameters, not amplitude in the ideal model.
What should I identify before using an equation?
Relate period T and frequency f, then compare how spring-mass and small-angle pendulum periods change when mass, spring constant, pendulum length, or gravitational field strength changes.
Where do I practice this exact topic?
Use the 42-MCQ and 4-FRQ Topic 7.2 banks linked directly on this page.
Where Topic 7.2 appears in AP-style released work
These are original topic summaries and alignment notes, not reproduced College Board question text. One released FRQ can legitimately connect to several topics.
Spring-mass oscillation and position-time graph
Connects SHM period, spring constant and graphical analysis.
Mathematical RoutinesCollision with spring and oscillation-period comparison
Cross-unit momentum, spring and SHM connection.
Mathematical RoutinesPendulum comparison, work and elastic restoring behavior
Connects gravitational context, work/energy and oscillator period reasoning.
Qualitative / Quantitative TranslationRecent public FRQs are the safest format reference. Older released questions can still contain excellent physics, but the course and exam changed; use the atlas alignment notes before treating a legacy question as a current-format simulation.