Determining the oscilation of a ruler resting on two spinning cylinders

[daffy]

Homework Statement

A 75 gram ruler is evenly placed between two cylinders spinning clockwise on the left and counter clockwise on the right. The coefficient of friction between the ruler and the spinning cylinders is 0.2. You push the ruler to the right by 0.12 meters. It returns to you by moving left and continues past it's starting point, going a total of 0.11 meters to the left.

What is the frequency of oscillation of the ruler?

Homework Equations

We are given the equation for simple harmonic motion. We are not expected to use any differential equations in this physics course.

The equation of the location of the ruler is x(t) = A*cos(ωt+$\phi$)

The Attempt at a Solution

I drew a force body diagram by of the ruler resting on each spinning cylinder, but I found that the force of both of the cylinders cancels out. In addition, I don't know how to find the acceleration of the hand pushing the ruler, so I don't know how to find the force of the hand.

I'm mainly looking for some help getting this problem started. I'm having trouble conceptualizing this in a way that I can use it to get an answer.

 

[tiny-tim]

hi daffy!

… I found that the force of both of the cylinders cancels out. In addition, I don't know how to find the acceleration of the hand pushing the ruler, so I don't know how to find the force of the hand.

the reaction forces will be different (and therefore so will the friction forces)

and you can assume that the hand pushes gently, and releases the ruler when its speed is zero