SHM - problem with static friction

[SillySylar]

Homework Statement

A child with poor table manners is sliding his 243 g dinner plate back and forth in SHM with an amplitude of 0.109 m on a horizontal surface. At a point a distance 6.70×10−2 m away from equilibrium, the speed of the plate is 0.250 m/s.
a) What is the period?
b) What is the displacement when the speed is 0.152 m/s?
c) In the center of the dinner plate is a carrot slice of mass 10.7 g. If the carrot slice is just on the verge of slipping at the end point of the path, what is the coefficient of static friction between the carrot slice and the plate?

Homework Equations

A = sqrt(x^2 + (v^2/w^2))

The Attempt at a Solution

I tried the above equation and solved the period and the displacement questions with no problem. However, I really don't know where to start with the last one. Could someone give me some insight please? This homework is in the chapter of "Periodic motion", I'm not sure how to link it to the static friction =(

thank you all for your help, really appreciate it!

 

[Doc Al]

In order for the carrot to not slip it must have the same motion--and thus acceleration--as the plate. But the only horizontal force accelerating the carrot is static friction from the plate. What maximum value of static friction is required? What does that tell you about the minimum coefficient of static friction?

 

[lzkelley]

When they say "on the verge of" it means set the force of friction = to the other force acting on it. So in this case, the acceleration of the plate at the end of the path = F/m = the force of friction / m
Note that the acceleration is at a maximum at the end of the path.
Cool?

 

[SillySylar]

so basically F = ma => k x N = k m g = m a => k = a / g

I got the correct answer using that expression below. Thanks a ton guys :)