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 .
Conservation of energy
The Attempt at a Solution
Before hitting the bob, the expressions are mgh1+.5mv^2=mgh2+.5mv2^2
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?