Take the tour ×  I can find the energy of a spring using $F =
-kx$, or by using the formula $e = 1/2mv^2 + 1/2I\omega^2 + mgh
+ 1/2kx^2$. The first way, I get $mg/k = x$, but the second way,
I get $2mg/k = x$. Which one is correct to use and why?  This is
assuming that there is no angular velocity or linear velocity.
share|improve this question add comment  1 Answer  The first
answer is correct, because if you let go of the spring and it
doesn't move, it means the total force on it is zero, so
$mg=kx$.  To understand why the second answer is incorrect,
think about what happens when you start at $x=0$, where $e=0$,
and let go of the spring. Suppose for now that mechanical energy
is conserved like you did. The spring will start falling down
and get stretched, until it reaches the point $x'$ that you
wrote down with $v=0$. But then it will get pulled back up, and
proceed to bob up and down. This shows that at $x'$ the total
force is not zero -- otherwise the spring would not get pulled
back up.  If there is no