# What is the maximum amplitude of oscillation of the system

1. Oct 5, 2009

### songoku

1. The problem statement, all variables and given/known data
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?

2. Relevant equations
$$a=-\omega ^2*A$$

$$\omega = 2\pi f$$

3. 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

2. Oct 5, 2009

### Delphi51

Re: oscillation

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

3. Oct 6, 2009

### songoku

Re: oscillation

Hi Delphi51

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

4. Oct 17, 2009

### SAT2400

Re: oscillation

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

which is right??

5. Oct 20, 2009

### songoku

Re: oscillation

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