Energy stored in an object in spring

Question

Suppose we have a vertical spring of spring constant $k$ and an object of mass $m$ is tied to it. If we stretch the object by a distance $x$,the work done by the restoring force is $\frac{kx^2}{2}$ and this work will be stored in the object as energy. If we try to find out what is the energy stored in the object now,why do we say it's $\frac{kx^2}{2}$ and not $\frac{kx^2}{2}+mgh$ since the body has also a potential energy? Addenum: We can see that the spring has done negative work on the body since the work done by spring is $$\int \vec{F}.d\vec{x}=\int -kx dx$$. Now doesn't negative work mean energy has been taken away from the body? Then how can it be stored in the body?

Answer 1

Both $mgh$ and $\frac{1}{2}kx^2$ are potential energies, so the total energy "stored" in the object is the sum of those two terms, assuming no other force in applied and the objet is at rest.