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 oscillation without relative motion between the blocks.
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.