← all cardsTopic 8 · Oscillations · Energy
The three energies
● VERBATIM — examined word-for-wordTotal energy is constant (undamped) and proportional to amplitude² and to f² — double x₀ → four times E.
KE = ½mω²(x₀² − x²) · PE = ½mω²x² · E_total = ½mω²x₀² = ½m v_max²What this actually means
Kinetic and potential energy trade back and forth with a constant total (undamped): all kinetic through the centre, all potential at the extremes.
The total is ½mω²x₀², so energy scales with amplitude squared and with frequency squared. Double the amplitude and the energy quadruples.
All three formulas are one identity rearranged: KE = E_total − PE. Learn one, derive the rest.
The trap
Halving the amplitude and halving the energy — E ∝ x₀², so it quarters.
Prove it — watch it be true
- Watch the energy bars: KE full at the centre, PE full at the extremes
- The total bar never moves while damping is off
- Turn damping on: now the total drains — the constancy was the undamped assumption