Friction problem Does this make sense?

[armolinasf]

Homework Statement

There are two masses stacked on top of each other. The bottom one, M, is attached to a spring with force constant k. The coefficient of static friction between the M and the top mass, m, is w. What is the maximum amplitude of oscillation such that the top box will not slip on the bottom.

The Attempt at a Solution

Initially my reasoning was that the force of friction, wn, where n is the normal force acting on the top box equal to mg, must equal the pulling force, f=kx

wmg=kx then x=(wmg)/k. The answer in my book gives x= (w(m+M)g)/k

I'm not sure if the way I arrived at that answer is correct:

F=kx=(m+M)a ==> a1=kx/(m+M)

wmg=kx ==>wg=kx/m=a2

But a2 is really equal to a1 since that's the box that's what's being accelerated.

wg=kx/(m+M) ==>w(m+M)g/k = x

I just want to be sure that makes sense. Thanks for the help

 

[Dick]

Looks ok to me. You need the mass on the top not to slip at the point of maximum acceleration, which is when x is at its maximum value of oscillation.