Simple Harmonic Motion and Static Friction. I am stumped.

[IWuvTeTwis]

Homework Statement

During an earthquake, a floor oscillates horizontally in approximately simple harmonic motion. Assume it oscillates at a single frequency with a period of 0.84 s.

After the earthquake, you are in charge of examining the video of the floor motion and discover that a box on the floor started to slip when the amplitude reached 15 cm. From your data, determine the coefficient of static friction between the box and the floor.

Homework Equations

F=ma
Maximum Fs = mg(coef of fric)
F=kx
x=A since we can set t=0 since we are finding maximum acceleration, so F=kA
w = 2pi/T
x=Acos(wt)
a=-Aw^2cos(wt)
a=-w^2*x

The Attempt at a Solution

I realize that the maximum force of static friction equals the force of the oscillation. We can either relate that as Fs = ma or Fs = kx. However, both of those contain two unknowns. I cannot seem to find a way to get rid of either the k or m term, which is my problem.

 

[ideasrule]

F=ma
Maximum Fs = mg(coef of fric)
F=kx

F=kx is the force that a spring experiences when displaced by "x". In this case, the "spring" is Earth's crust, but we don't care what force Earth's crust experiences.

w = 2pi/T
x=Acos(wt)
a=-Aw^2cos(wt)
a=-w^2*x

This is correct, and you can see that the maximum possible value of a is w^2*A. Now you just need to find the friction force needed to make the box accelerate at this rate.

 

[IWuvTeTwis]

Thank you for the help, I figured out how to do it.