# Understanding an equation in a dynamics spring problem

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1. Apr 30, 2017

### Bunny-chan

1. The problem statement, all variables and given/known data
A block of mass $M = 0.5kg$, attached to a spring of elastic constant $k = 3N/m$ on a vertical wall, slides without friction through an horizontal air table. A disk of mass $m = 0.05kg$ is placed on the block, whose surface has a coefficient of static friction $\mu _e = 0.8$. What is the maximum oscillation amplitude of the block so the disk won't slide off of it?

2. Relevant equations
$\vec F = m\vec a \\ \vec F = -kx \\ F_{\mu e}^{max} = \mu _emg$
3. The attempt at a solution
I have already solved this problem, and then I've checked part of a solution on the web containing an insight on the theory behind it:

I don't really understand the second part where the author talks about the non-inertial frame reference, and about the forces involving it, and ends up with the equation

Even though I was able to solve the exercise, I reached the last equation through a more direct way, without thinking too much about it, so this explanation made me a bit confused. Am I being clear enough?

I hope someone can help!

2. May 1, 2017

### haruspex

There are cases where noninertial frames make life simpler, but this is not one of them. The sign of a is irrelevant since reversing it just leads to the other extreme of x, so it matters not whether you write a=μeg or a=-μeg. This same equation arises whether you think in terms of an inertial frame or a noninertial one.

3. May 1, 2017

### Bunny-chan

Hmm. I think I get it. So this is why in these equations we don't really take into account the negative signs? Because we're just interested in the value?

4. May 1, 2017

### haruspex

No, I'm saying that both signs are correct for maximum displacement; but the question asks for amplitude, which is by definition the magnitude of the maximum displacement, so non-negative.

5. May 1, 2017

### Bunny-chan

OK. I see. Thank you.