Simple Harmonic Motion
Oscillations like springs and pendulums follow sine waves.
About this topic
Simple harmonic motion is repeating back-and-forth movement where the restoring force is proportional to the displacement, such as a mass on a spring or a small pendulum swing. Its position follows a sine or cosine curve: x = A cos(ωt + φ).
Amplitude A is the maximum displacement, ω is the angular frequency in radians per second, the period is T = 2π/ω and the frequency is f = 1/T. For a spring, ω = √(k/m), so stiffer springs oscillate faster and heavier masses slower; for a small-angle pendulum, ω = √(g/L). The speed is greatest as it passes through the centre and zero at the extremes, where the acceleration is largest.
Example: a 0.5 kg mass on a spring with k = 50 N/m has ω = 10 rad/s, a period of about 0.63 s and a frequency of 1.6 Hz, regardless of how far it is stretched.
This model describes guitar strings, clocks, vibrating atoms, bridges and AC circuits. A common misconception is that a bigger swing takes longer; for ideal systems the period does not depend on amplitude. Real systems lose energy through damping, so the amplitude gradually shrinks.
Key ideas
- x(t) = A sin(ωt + φ)
- Period T = 2π/ω
- Amplitude A is the maximum displacement
Quick check
Use cases: where Simple Harmonic Motion helps
- Homework: review the key idea behind Simple Harmonic Motion before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Simple Harmonic Motion without notes.
- Visual learning: play with the interactive lab to see how Simple Harmonic Motion changes when you adjust its inputs.
- Teaching a friend: explain Simple Harmonic Motion in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Simple Harmonic Motion?
Oscillations like springs and pendulums follow sine waves.
What will I learn in Simple Harmonic Motion?
x(t) = A sin(ωt + φ). Period T = 2π/ω. Amplitude A is the maximum displacement.
Is Simple Harmonic Motion part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Simple Harmonic Motion lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Simple Harmonic Motion?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.