Past exam of the physics course of the year 1 of the natural sciences course of the University of Cambridge / 2024 / Paper 1 / Section B / 8 / d / Solution

For weak linear damping, write the amplitude envelope as $A(t)=A_0{e}^{-{\omega }_{0}t/(2Q)}$. The amplitude e-folding time is $2Q/{\omega }_0$, and one period is approximately $2\pi /{\omega }_0$. ThusEnergy, being proportional to amplitude squared, decays twice as rapidly in its exponent. Using its e-folding time instead would introduce a factor-of-two error.