Problem 6.18

In accordance with classical electrodynamics an electron moving with acceleration w loses its energy due to radiation as \[ \frac{d E}{d t}=-\frac{2 e^{2}}{3 c^{3}} \mathrm{w}^{2} \] where \(e\) is the electron charge, \(c\) is the velocity of light. Estimate the time during which the energy of an electron performing almost harmonic oscillations with frequency \(\omega=5 \cdot 10^{15} \mathrm{~s}^{-1}\) will decrease \(\eta=10\) times.