1. The problem statement, all variables and given/known data I have small block of mass m=1kg on top of a bigger block mass M=10kg The friction coefficient between the blocks μ=0.40 No fricton between the big block and the ground. There is a spring with k=200N/m attached to the bigger block. The problem asks what is the maximum amplitude A the system can have in an harmonic oscilation without relative motion between the blocks. 2. Relevant equations [itex]x=A\cos(ωt+\phi)[/itex] [itex]v=-ωA\sin(ωt+\phi)[/itex] [itex]a=-ω^2A\cos(ωt+\phi)[/itex] 3. The attempt at a solution well, first I noticed that the maximum static force possible between the two blocks will be: mgμ which gives: [itex](1kg)(9.8m/s^2)(0.40) = 3.92N[/itex] so far no problems I guess. using F=ma, I calculate the acceleration of the system in the case of maximum friction: [itex]a= F/m = (3.92N)/(11kg)[/itex] which gives [itex]a = 0.356m/s^2[/itex] using [itex]ω^2=k/m=(200N/m)/(11kg)[/itex] which gives [itex]ω^2= 18.18rad/s^2[/itex] Now here is where I got stuck I plug this to [itex]a=-ω^2Acos(ωt+\phi)[/itex] and try solving for A the thing is: I don't know the time I don't know if there is a phase angle involved or not. or how to find out.