1. The problem statement, all variables and given/known data After four cycles the amplitude of a damped harmonic oscillator has dropped to 1/e of it's initial value. Find the ratio of the frequency of this oscillator to that of it's natural frequency (undamped value) 2. Relevant equations x'' +(√k/m) = 0 x'' = d/dt(dx/dt) x'' + 2βx' + Wo^2= 0 Here we are assuming a damping force linear in v, f = -bv 2β is defined as b/m where b is a constant. Wo^2 = k/m 3. The attempt at a solution Since the problem statement makes no mention of whether this is underdamped (β then than Wo), overdamped (β greater than Wo), or critically damped (β= Wo), I can only conclude that it does not matter what the case is. Two of the solutions can be expressed as sines and cosines and would be periodic with 2∏, but one of the solutions is simply two exponential terms, which does not make sense to me. That's kind of where I'm stuck, any thoughts would be helpful. Thanks.