Energy in SHM
BINAS 35B1Tsokos Ch. 9.4
Overview
Total mechanical energy E = ½kA² = constant (no damping). KE and PE continuously exchange. At equilibrium (x = 0): KE is maximum, PE = 0, speed = v_max = ωA. At amplitude (x = ±A): KE = 0, PE is maximum, speed = 0. KE = ½m(ωA)² − ½mω²x² = ½mω²(A²−x²). PE = ½kx² = ½mω²x².
Energy in SHM — KE and PE exchange
In SHM, energy continuously exchanges between kinetic energy (KE) and potential energy (PE), with the total mechanical energy E remaining constant (no friction). PE is maximum at the amplitude: PE_max = ½kA² = ½mω²A². KE = 0 at x = ±A. At equilibrium: KE is maximum = ½mω²A², PE = 0. At any position: KE = ½mω²(A² − x²), PE = ½mω²x².
Worked Examples
Common Mistakes
- ⚠Using ½mv² to find total energy — this only gives KE at a specific instant, not total E
- ⚠Forgetting E ∝ A² (not A) — doubling amplitude quadruples total energy