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Darkalyan
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Homework Statement
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:
http://docs.google.com/Doc?id=d277r7r_54dgf3xhgb&hl=en
Homework Equations
U=integral (F,dx)
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?
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