Maximum amplitude of oscillation of a block

[Mac13]

I've been staring at this problem for a loonnng time and i just can't figure it out:(.. i would appreciate it if someone could help me...thx! :)

A large block with mass 26 kg executes
horizontal simple harmonic motion as it slides
across a frictionless surface with a frequency
1:9 Hz : Block smaller block with mass 9 kg
rests on it, and the
coefcient of static friction between the two is
u = 0.459.
The acceleration of gravity is 9:8.
What maximum amplitude of oscillation
can the system have if the block is not to slip?
Answer in units of cm.

 

[HallsofIvy]

The weight of the smaller block is 9(9.81) = 88.29 Newtons. The force necessary to overcome the static friction, then is (88.29)(0.459)= 40.52 Newtons. Using "F= ma", that would correspond to an acceleration (of the smaller) block of 40.52= 9a or
a= 4.50 m/s². What amplitude would give a maximum acceleration no greater than 4.5 m/s²?

 

[Mac13]

thanks...its a little too late to turn it in for my homework because it was due early this morning but at least i understand it now:)