Weight attached to a spring general question?

MathWarrior
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I was wondering, in my class we have been dealing with a lot of equations related to some weight attached to a spring which is attached to a fixed point and has some force being applied to it or something like that. Where exactly is such a thing encountered in real life?
 
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lots of weighing machines

things like car suspensions (except upside-down)
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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