Suppose a spring is on a surface.An An object of mass $m$ is in $h$ meter height from the top of the spring.When When the object falls freely,the the spring contracts by $x$ meter.Find Find $x$ when $k$ is spring constant.
The solution given in books is $mg(h+x)=\frac{1}{2}kx^2$.
Now,let us consider the top of the spring as reference plane.So So potential energy at that plane is $0$.Now Now energy of the system at the beginning is only the potential energy of the object.So
So $E_1=mgh$
After the fall,the spring contracts by $x$ meter,so so the potential energy of the spring is now $\frac{1}{2}kx^2$ and the potential energy of the object is $-mgx$ and kinetic energy of the object is
$\frac{1}{2}mv^2$.
So by conservation of energy,we get
$mgh=-mgx+\frac{1}{2}mv^2+\frac{1}{2}kx^2$.
Where did I go wrong?