- #1

Emethyst

- 118

- 0

## Homework Statement

A block with mass M rests on a frictionless surface and is connected to a horizontal spring of force constant k, the other end of which is attached to a wall. A second block with mass m rests on top of the first block. The coefficient of static friction between the blocks is u. Find the maximum amplitude of oscilliation such that the top block will not slip on the bottom block.

## Homework Equations

Hooke's Law (F = -kx), F = ma

## The Attempt at a Solution

So far what I managed to do is get two F

_{net}equations, setting the lefthand direction as the negative direction (this being the direction of the spring force and acceleration). The first F

_{net}equation is (m + M)(a) = -F

_{spring}and the second 0 = umg - F

_{spring}, or umg = F

_{spring}. After this I start encountering problems. I am supposed to end up with x =(ug(m + M))/k as the equation to find the maximum amplitude, but I end up with x = umg/k for in Hooke's Law I first found acceleration: a = -kx/m, then made m = m + M, and finally subbed all three equations together and solved for x. Can someone point out where I'm going wrong here and show me the correct way to derive the correct formula? Any help would be greatly appreciated.