PhysicsChapter 3: Simple Harmonic Motion
Circular Motion and SHM
Simple harmonic motion can be represented as the projection of uniform circular motion onto a diameter of the circular path.
Definition
Simple harmonic motion can be represented as the projection of uniform circular motion onto a diameter of the circular path.
Formula / Key Relation
Consider a particle moving uniformly around a circle of radius `A` with angular speed `ω`. Its projection on a diameter moves backward and forward. If angular position is: θ = ωt + φ then projection on the x-axis is: x = A cosθ Therefore: x = A cos(ωt+φ) This is the displacement equation of SHM. The radius of the circle corresponds to SHM amplitude. One complete revolution corresponds to one complete oscillation. Therefore: T = 2π/ω and: f = ω/2π **x=A cos(ωt+φ) T=2π/ω f=ω/2π**
Exam preparation
Exam Focus
Quick revision
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Review the key facts, formulas and checks before you move on.Circular Motion and SHM
Sticky Notes · Quick Revision
Circle radius → `A`
- Angular speed → `ω`
- Projection → SHM
- One revolution → one oscillation
60-second revision
- SHM is mathematically equivalent to one-dimensional projection of uniform circular motion.
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