1. The problem statement, all variables and given/known data The amplitude of an underdamped oscillator decreases to 1/e of its initial value after m complete oscillations. Find an approximate value for the ratio ω/ω0. 2. Relevant equations x''+2βx'+ω02x = 0 where β=b/2m and ω0=√(k/m) x(t) = Ae-βtcos(ω1t-δ) where ω1 has been defined as ω02-β2 3. The attempt at a solution The initial amplitude is equal to A0 = Ae-βt and the final amplitude after m oscillations is equal to A0(1/e) = Af = Ae-(βt+1) After this I honestly don't know where to go. I tried plugging in my Af into the underdamped motion equation and solving for ω but that didn't seem to make any sense. I'm assuming that ω0 will be equal to just √(k/m)? Also, I thought that the frequency of an underdamped oscillator didn't change over time. So why would the angular frequency change? If anyone could give me a push in the right direction that would be very helpful. I've been working on this for a quite while now.