PhysicsChapter 3: Simple Harmonic Motion
Displacement, Velocity and Acceleration in SHM
In SHM, displacement, velocity and acceleration vary periodically with time and have fixed mathematical relationships.
Definition
In SHM, displacement, velocity and acceleration vary periodically with time and have fixed mathematical relationships.
Formula / Key Relation
Take: x=A cos(ωt+φ) Differentiate: v=dx/dt Therefore: v=−Aω sin(ωt+φ) Velocity in terms of displacement: **v²=ω²(A²−x²) Hence: v=±ω√(A²−x²) Maximum velocity: vmax=Aω Differentiate velocity: a=dv/dt Therefore: a=−Aω²cos(ωt+φ)** Since: `x=Acos(ωt+φ)` we obtain: **a=−ω²x Maximum acceleration magnitude: amax=Aω² x=Acos(ωt+φ) v=−Aωsin(ωt+φ) v²=ω²(A²−x²) a=−ω²x vmax=Aω amax=Aω²**
Exam preparation
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Review the key facts, formulas and checks before you move on.Displacement, Velocity and Acceleration in SHM
Sticky Notes · Quick Revision
Centre:
- `x=0`
- `v=max`
- `a=0`
- Ends:
- `x=±A`
- `v=0`
- `|a|=max`
60-second revision
- Velocity peaks at equilibrium; acceleration peaks at extremes.
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