PhysicsChapter 3: Simple Harmonic Motion
Energy in SHM
In ideal SHM, energy continuously changes between **kinetic energy** and potential energy
Definition
In ideal SHM, energy continuously changes between kinetic energy and potential energy, while total mechanical energy remains constant.
Total Energy
For a spring: Potential Energy `U = ½kx²` Since: `k=mω²` we can also write: U = ½mω²x² At maximum displacement `x=A`, velocity is zero. Therefore: **E = ½kA² or: E = ½mω²A²**
Kinetic Energy
**K = E-U Therefore: K = ½mω²(A²-x²)**
At Equilibrium
`x=0` `U=0` `K=maximum`
At Extreme Positions
`x=±A` `K=0` `U=maximum`
Formula / Key Relation
**U=½mω²x² K=½mω²(A²−x²) E=½mω²A²**
Exam preparation
Exam Focus
Quick revision
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Review the key facts, formulas and checks before you move on.Energy in SHM
Sticky Notes · Quick Revision
Equilibrium:
- KE max
- PE min
- Extreme:
- KE zero
- PE max
60-second revision
- Ideal SHM conserves mechanical energy.
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