← all cardsTopic 10 · 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
- Read KE, PE and Total against displacement: KE fills at x = 0, PE fills at x = ±x₀, and Total is flat right across the range
- Press the E ∝ x₀² doubling button: doubling the amplitude makes Total four times as tall, not twice
- Press the E ∝ f² doubling button: doubling f quadruples it too — both squares of E = ½mω²x₀²