What is the maximum amplitude of oscillation of the system

[songoku]

Homework Statement

A large block P executes horizontal simple harmonic motion as it slides across a frictionless surface with a frequency f = 1.5 Hz. Block B rests on it, as shown in the figure, and the coefficient of static friction between the two is 0.6. What is the maximum amplitude of oscillation of the system so that block B dos not slip?

Homework Equations

$$a=-\omega ^2*A$$

$$\omega = 2\pi f$$

The Attempt at a Solution

$$a=\omega ^2*A$$

$$\frac{F}{m}=(2\pi f)^2*A$$

$$A=\frac{\mu _s*N}{m*(2\pi f)^2}$$

$$A=\frac{\mu _s*mg}{m*(2\pi f)^2}$$

$$A=6.62~cm$$

Do I get it right?

Thanks

 

[Delphi51]

It looks good to me!
I haven't seen that acceleration formula before, so I'm no expert on this.

 

[songoku]

Hi Delphi51

It's formula for maximum acceleration of simple harmonic motion. Thanks a lot for your reply.

 

[SAT2400]

a = - w^2 * A or a = w^2 *A??

which is right??

 

[songoku]

a = - w^2 * A or a = w^2 *A??

which is right??

$$a=-\omega ^2 A$$ is right because acceleration is vector. The negative sign indicates that the direction of the acceleration is in the opposite direction of the direction of motion of the particle.

In my case, I just need the numerical value so I omit the negative sign