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## Homework Statement

A large block P executes horizontal simple harmonic motion by sliding across a frictionless surface with a frequency f = 1.5 Hz. Block B rests on it, and the coefficient of static friction between the two is [tex]\mu_s=0.60[/tex]. What maximum amplitude of oscillation can the system have if the block is not to slip?

## Homework Equations

[tex]F=-kx=ma[/tex]

[tex]a=-\frac{k}{m}x[/tex]

## The Attempt at a Solution

I'm not positive that i need the equations above, but I do know that the amplitude will be given by [tex]\frac{\mu_sg}{4\pi^2f^2}[/tex] according to the textbook answer. The numerical value comes out to be 0.662 m. But I'm not sure how to associate the forces with the harmonic motion exactly. I was thinking that somehow the force must not be greater than than [tex]\mu_smg[/tex] since that is what the maximum friction force allowed would be. But I'm not sure if I need to work with the motion equations for harmonic motion or if I need to use some method involving the period, forces, etc. Any pointer in the right direction would be much appreciated.

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