1. The problem statement, all variables and given/known data Consider 2 oscillators (mass attached to spring on surface). For one oscillator, the surface is frictionless, but there is viscous damping (f=-bv). For the other, the surface has coefficient of kinetic friction uk, but there is no viscous damping. The masses are both pulled away from the equilibrium the same distance then released. When they first reach the equilibrium position, the magnitude of the viscous damping force for the first oscillator is equal to the magnitude of the frictional force for the second oscillator. which oscillator damps down to 1/10 the initial amplitude more quickly? 2. Relevant equations F=-bv (viscous damping at slow speeds) F=uk×N=uk×mg (force of friction) x=Ae^(-σt)cos(ωt+∅) 3. The attempt at a solution The decaying envelope function e^(-σt) determines the degree of damping. The term Ae^(-σt) acts as a varying amplitude. I defined Ae^(-σt) to be the amplitude of the oscillator subject to viscous damping and Ae^(-βt) to be the amplitude of the oscillator with no viscous damping. By setting .1A=Ae^(-σt) and .1A=Ae^(-βt) and solving for t in both cases I could get the time taken for each oscillator to decay to .1A in terms of σ and β. Time taken for oscillator subject to viscous damping=t1=ln(.1)/-σ and the time taken for the other oscillator=t2=ln(.1)/-β. I have two equations and four unknowns. I know that for the oscillator subject to viscous damping σ=b/2m where m is the mass and b is the damping coefficient.