Oscillations
What this unit covers
The topics below follow the published Physics 1 course framework for Unit 7. This unit is worth 5–8% of the exam, so budget your time against that rather than against how long the unit takes to teach.
Lessons in this unit
- Simple Harmonic Motion & Springs13 min · 3 objectivesDefine simple harmonic motion and the restoring force · Apply Hooke’s law, F = −kx · Locate where speed and acceleration are greatest in an oscillation
- Pendulums13 min · 3 objectivesDescribe a simple pendulum as SHM for small angles · Apply the pendulum period formula, T = 2π√(L/g) · Identify what does and does not affect a pendulum’s period
- Period & Frequency12 min · 3 objectivesDefine period and frequency and their reciprocal relationship · Convert between period and frequency · Interpret oscillation counts over a time interval
- Energy in Simple Harmonic Motion13 min · 3 objectivesDescribe the continual exchange between elastic PE and KE · Use total energy ½kA² to find the maximum speed · Relate the total energy of an oscillator to its amplitude
Formulas in Unit 7
Every term in Unit 7
All 13 terms we publish for Oscillations, with definitions. Reading them through is the fastest way to find the ones you cannot define — then drill those in cram mode until you can produce them without the prompt.
- Simple harmonic motion
- Motion where the restoring force is proportional to displacement and directed toward equilibrium: F = −kx.
- Period and frequency
- T is seconds per cycle, f is cycles per second, and T = 1/f. Angular frequency ω = 2πf.
- Mass-spring period
- T = 2π√(m/k). Independent of amplitude — a wider swing simply moves faster.
- Simple pendulum period
- T = 2π√(L/g), valid for small angles. Independent of mass and, for small amplitude, of amplitude.
- Energy in SHM
- Total energy is constant; it is all elastic PE at maximum displacement and all KE at equilibrium, exchanging continuously between them.
- Velocity and acceleration in SHM
- Speed is maximum at equilibrium where acceleration is zero; acceleration is maximum at the extremes where speed is zero.
- Amplitude independence
- Period does not depend on amplitude in ideal SHM, which is what makes pendulums useful as clocks.
- Damping
- Dissipative forces reduce amplitude over time while leaving the period almost unchanged for light damping.
- Determining k from a graph
- The slope of a force vs displacement graph for a spring is the spring constant.
- Why T is independent of amplitude
- A larger amplitude means a larger restoring force and hence greater speed, and the two effects cancel exactly for a linear restoring force.
- Period from a T² graph
- Plotting T² against m for a mass-spring system gives a straight line of slope 4π²/k, which is how k is measured experimentally.
- Phase in SHM
- Displacement, velocity and acceleration are each a quarter-cycle out of step: velocity peaks where displacement is zero, acceleration where displacement is extreme.
- Pendulum on another planet
- T = 2π√(L/g), so a pendulum swings more slowly where g is smaller. Timing one is a way to measure g.
What examiners penalize here
- A frequent SHM question asks "where is acceleration maximum / speed maximum?" Remember they are opposite: acceleration peaks at the extremes (max force), speed peaks at equilibrium (max KE).
- To change a pendulum’s period you must change its length or move it to a different g. Adding mass or (for small swings) changing the amplitude does nothing — a common distractor on the exam.
- Keep the units straight: period is seconds *per* cycle, frequency is cycles *per* second. When a problem gives "cycles in a time," divide cycles by time for frequency, then invert for period.
- The total energy of an oscillator scales with the *square* of the amplitude (E = ½kA²). Double the amplitude and you quadruple the energy — and the maximum speed only doubles, since v_max scales linearly with A.
Practice Physics 1
Our practice bank is drawn from across the whole course rather than filtered to one unit, which is closer to how the exam asks anyway — it will not tell you which unit a question is testing.
Questions about this unit
How much of the AP Physics 1: Algebra-Based exam is Unit 7?
Unit 7, Oscillations, is worth 5–8% of the Physics 1 multiple-choice section according to the published course framework. Across all 8 units that makes it a middling share, roughly what an even split across units would give.
What topics are covered in Physics 1 Unit 7?
Oscillations covers Springs, Pendulums, Period & frequency and Energy in SHM. We publish 13 terms with definitions for this unit, all of them on this page.
How should I study Physics 1 Unit 7?
Read the 4 lessons below first — about 50 minutes — then drill the 13 terms in cram mode until you can produce each definition from memory rather than just recognize it. Recognition is what makes a unit feel finished when it is not. Finish with practice questions and read the explanation for every one you get right by elimination as well as the ones you miss.
All 8 units of AP Physics 1: Algebra-Based
Unit names, topics and exam weights follow the published College Board course framework for AP Physics 1: Algebra-Based. AP® is a trademark registered by the College Board, which does not endorse this site.