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I've been given that there is a spring holding a $.25kg$ mass where $k=10N/m$ and is held at $40cm$ and then let go. I've found that the max velocity is $2.53m/s$ and that when the spring is at $20cm$ the velocity is $2.19m/s$

What I'm having a hard time wrapping my head around is finding the position when the kinetic energy and potential energy are equal.

I keep trying to arrange it like so but end up with two unknowns

$.5(10N/m)(\Delta x)^2 = .5(.25kg)v^2$

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closed as off-topic by Qmechanic Mar 21 '18 at 6:17

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You know that energy is always conserved so at the point where $U$ and $K$ are equal a.k.a $$U = K$$, you also know that $$U + K = \text{Total Energy}$$. Now you have two variables two equations and I'll leave the rest for you to solve :D Good Luck! Does this help?

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