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

AI Thread Summary
The discussion revolves around determining the amplitude of simple harmonic motion that causes a smaller block to slip over a larger block in a two-block spring system. The system consists of two blocks with specified masses and a spring with a known spring constant. The coefficient of static friction is provided, but the coefficient of kinetic friction is not, raising concerns about calculating the acceleration of the top block once slipping occurs. The key point is that only the static friction coefficient is necessary to find the amplitude at which slipping begins, making the dimensions of the blocks irrelevant. The focus remains on the relationship between the spring's force and the static friction to establish the critical amplitude for slippage.
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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?

acom=F/(mA+mB)

F=-kAcos(ωt) and ω=√(k/(mA+mB)= 4.26

so F=-200Acos(4.26t)

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

This is all I got so far. What I am confused about is that μk 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.
 
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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.
 
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