# Compression distance

1. Apr 2, 2013

### fredrogers3

1. The problem statement, all variables and given/known data
F= -kx-bx^3 of the spring

A pendulum bob of mass m is raised to a point h and released.After hitting the
non-linear spring, calculate the compression distance of the spring as function of k ,
b , m , g , and h .
Picture here:http://www.chegg.com/homework-help/...-3--work-compressing-spring-distance--q237651

2. Relevant equations
Conservation of energy

3. The attempt at a solution
Before hitting the bob, the expressions are mgh1+.5mv^2=mgh2+.5mv2^2
V2=sqrt 2gh
At the moment it hits the bob, .5mv2^2=.5kx3^2+.25kx3^4

By the end of simplifying, .5kx3^2+.25bx3^4 - mgh
I am to solve for x3, but when I do it comes out as a complicated expression with a couple of square roots in it. I took y=x^2, by the way, in order to use the quadratic formula. Am I correct in my work?

Last edited: Apr 2, 2013
2. Apr 2, 2013

### voko

Yes, you should have a complicated expression with a couple of roots in it. It will have b, k, m, g, h, too. Your method looks generally correct (except you seem to have lost b along the way).