What Amplitude Causes Slippage in a Two-Block Spring System?

[Fizic]

Two blocks (m=1.0 kg and M=10 kg) and a string (k=200 N/m) are arranged on a horizontal, frictionless surface (in the picture m rests atop M). The coefficient of static friction between the two blocks is .40. What amplitude of simple harmonic motion of the spring-blocks system puts the smaller block on the verge of slipping over the larger block?

a_com=F/(mA+mB)

F=-kAcos(ωt) and ω=√(k/(mA+mB)= 4.26

so F=-200Acos(4.26t)

a_com=-200Acos(4.26t)/11
=-18.2Acos(4.26t)

This is all I got so far. What I am confused about is that μ_k is not given. So isn't it impossible to figure out the acceleration of the top block once static friction is overcome? I also am not given the lengths of the blocks.

 

[haruspex]

The question means, at what amplitude would it start to slip? For that you only need static friction coefficient, and the block widths are irrelevant.