Compression Distance Calc of Spring: F=-kx-bx^3

[fredrogers3]

Homework Statement

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/questions-and-answers/1-spring-obeys-non-linear-force-law-f-8722-kx-8722-bx-3--work-compressing-spring-distance--q237651

Homework Equations

Conservation of energy

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?

 

[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).