Simple Harmonic Motion
Oscillation modelled by sine or cosine.
Key idea
Oscillation modelled by sine or cosine.
In depth
In SHM the restoring force is proportional to the displacement, producing x(t) = A cos(ωt + φ). The period T = 2π/ω is independent of the amplitude. Springs and pendulums at small angles follow it.
Worked example
A mass on a spring with ω = 2 rad/s has period π ≈ 3.14 s.
Formula
Real-world uses
- Modelling a mass on a spring, a swinging pendulum and vibrations in car suspension
Common mistake
Thinking a larger swing takes longer in SHM. The period is independent of the amplitude.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Simple Harmonic Motion?
Oscillation modelled by sine or cosine. It is a topic at the advanced level in Trigonometry.
What is the formula for Simple Harmonic Motion?
The key formula is x(t) = A cos(ωt + φ).
Where is Simple Harmonic Motion used in real life?
Real-world examples: Modelling a mass on a spring, a swinging pendulum and vibrations in car suspension.
What should I learn before Simple Harmonic Motion?
Make sure you are comfortable with Fourier Series Introduction, the previous topic in Trigonometry.
What is a common mistake with Simple Harmonic Motion?
Thinking a larger swing takes longer in SHM. The period is independent of the amplitude.
How can I practise Simple Harmonic Motion?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Simple Harmonic Motion?
Move on to Sound Waves and Beats next.
Related advanced topics in Trigonometry
- Graph of Tangent – Periodic with vertical asymptotes at odd multiples of π/2.
- Phase Shift – Horizontal translation of a wave.
- Vertical Shift and Midline – Moves the wave up or down.
- General Sinusoid – Combine amplitude, period, phase and shift.
- Graphs of Reciprocal Trig Functions – Secant, cosecant and cotangent graphs.
- Pythagorean Identity – The key identity from the unit circle.