# Asymmetrical Linear Spring

1. Sep 23, 2008

### Darkalyan

1. The problem statement, all variables and given/known data
Consider an asymmetrical nonlinear spring whose force law is given by F=-kx+(k2)x^2 + (k3)x^3.

k=300
k2=300
k3=200
m=2
d=.5

Here's the problem statement as a google doc:

2. Relevant equations
U=integral (F,dx)
3. The attempt at a solution

a. It's called an asymmetrical spring because the force necessary to stretch the spring x units changes depending on how far the spring is from the origin. So basically, graphically, the force by distance graph looks like x^3, which is NOT symmetric about the y axis, thus the spring is asymmeetrical.

b. So, for this I thought what I could do was find the potential energy at the original distance of .5 meters. I would do this by integrating Fdx. Thus, U(.5)=16.66666
Now, I find U(.25), which is: U(.25)=6.7708333. Thus, KE=U(.5))-U(.25)=9.896

Thus, 9.896=mv^2/2, and m=2 kg, so I can solve for v using that equation, which would give me:

v=3.14157 m/s

Is that right?

Last edited by a moderator: May 3, 2017