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# Simple harmonic motion and maximum amplitude of oscillation

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A large block P executes horizontal simple harmonic motion as it slides across a frictionless surface with a frequency f. Block B rests on top of block P and the static coefficient of static friction between the two is mu_s. What maximum amplitude of oscillation can the system have if the upper block is not to slip?

I am not sure how to set this up to get the maximum amplitude. Do you add the masses of the block? Since it is oscillating how is mu_s figured into it?

##### Solution Summary

This solution is provided in approximately 312 words in an attached .doc and .pdf file. It provides equations for motion and acceleration of the block, and uses Newton's first and second law to describe the behaviour of the system and find maximum amplitude of oscillation.

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The solution is attached below in two files. The files are identical in content, only differ in format. The first is in MS Word XP Format, while the other is in Adobe pdf format. Therefore, you can choose the format that is most suitable to you.

The general motion of the block P can be described as:

Where  is the angular frequency and  is the phase shift to be determined from initial conditions.

Thus the block's acceleration ...

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