Compressed spring with work

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The force required to compress an imperfect horizontal spring an amount x is given by F = 150x + 12x3, where x is in meters and F in newtons. If the spring is compressed 2.0m, what speed will it give to a 3.0 kg ball held against it and then released?

I know how to integrate F(x) to get the work done, and with that I could use the work-energy theorem to find the speed. But do I take the lower limit of the integral as x = 2.0 and the upper limit as x = 0?
But then the integral would be negative and 1/2mv2 can't be negative...
 
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  • #2
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Are you finding the work function by solving [tex] F = -\frac{dU}{dx}[/tex]? I would integrate from x=0 to x=x to find the general solution, but if you wanted to put in 2 right away then that would work. The negative thing depends on where you define your zero potential.
 

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