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Compression distance

  1. Apr 2, 2013 #1
    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. jcsd
  3. Apr 2, 2013 #2
    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).
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