Given: The amplitude of a damped harmonic oscillator drops to 1/e of its initial value aft...

Given: The amplitude of a damped harmonic oscillator drops to 1/e of its initial value after n complete cycles. Show that the ratio of period of the oscillation to the period of the same oscillator with no damping is given by

where the approximation in the last expression is valid if n is large. (See the approximation formulas in Appendix D.)