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## Homework Statement

I have small block of mass

**m=1kg**on top of a bigger block mass

**M=10kg**

The friction coefficient between the blocks

**μ=0.40**

No fricton between the big block and the ground.

There is a spring with

**k=200N/m**attached to the bigger block.

The problem asks what is the maximum amplitude A the system can have in an harmonic oscilation without relative motion between the blocks.

## Homework Equations

[itex]x=A\cos(ωt+\phi)[/itex]

[itex]v=-ωA\sin(ωt+\phi)[/itex]

[itex]a=-ω^2A\cos(ωt+\phi)[/itex]

## The Attempt at a Solution

well, first I noticed that the maximum static force possible between the two blocks will be:

**mgμ**which gives: [itex](1kg)(9.8m/s^2)(0.40) = 3.92N[/itex]

so far no problems I guess.

using F=ma, I calculate the acceleration of the system in the case of maximum friction:

[itex]a= F/m = (3.92N)/(11kg)[/itex] which gives [itex]a = 0.356m/s^2[/itex]

using [itex]ω^2=k/m=(200N/m)/(11kg)[/itex] which gives [itex]ω^2= 18.18rad/s^2[/itex]

Now here is where I got stuck

I plug this to [itex]a=-ω^2Acos(ωt+\phi)[/itex] and try solving for A

the thing is:

I don't know the time

I don't know if there is a phase angle involved or not. or how to find out.

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