← all cardsTopic 8 · Oscillations · Energy
Damped: energy lost between amplitudes
● VERBATIM — examined word-for-wordAmplitude decays x₀₁ → x₀₂ (read two peaks off the graph) → energy lost to resistive forces:
ΔE = ½mω²(x₀₁² − x₀₂²)What this actually means
Read the amplitudes off two peaks of a decaying x–t graph; the energy surrendered to resistive forces between them is ½mω²(x₀₁² − x₀₂²).
It is nothing new: E ∝ amplitude squared, applied at two moments and subtracted.
The same formula reappears in Waves for a damped wave's envelope, so it pays double to own it here.
Prove it — watch it be true
- Turn damping on and let the motion decay
- Read the amplitudes of two chosen peaks
- Compare ½mω²(x₀₁² − x₀₂²) with the drop in the total-energy bar