The question is:
The lower end of a spring of spring constant $k$ is fixed on the ground and its other end passes through a light pulley and is connected to a block of mass $m$ after passing through the pulley. The system is released from rest. Find the maximum elongation of the spring. Initially the spring is unstretched.
I solved it using two different methods and I got different answers.
Let the maximum elongation of the spring be $x$. Then, the block also descends by a distance
x. So, increase in PE of the spring = decrease in PE of the block. So, $1/2kx^2=mgx$. This gives $x=2mg/k$.
At the maximum elongation of the spring, the system is in equilibrium. Let the module of the tension in the string be $T$. Then, since the block is at rest, so $T=mg$ when elongation is maximum. Also, the forces on the spring at equilibrium. are $kx$( due to elongation $x$) and $T$. So, $T=kx$, at equilibrium. So, $mg=kx$ or $x=mg/k$.
So, which of these two methods is wrong and why? Please answer.