A Question on Total Energy Calculation

Potential energy is energy by virtue of relative position of bodies (or parts of bodies). The bodies or parts of bodies are said to make up a system.

It's often convenient to choose one set of positions and call the potential energy zero for that configuration. For example when dealing with a body of mass $m_1$ near the Earth's surface we might take the gravitational potential energy as zero when the body is on the ground. When we lift it to a height $h_1$ the potential energy of the Earth–body system is $m_1gh_1$. For another body lifted to height $h_2$ then PE will be $m_2gh_2$.

For a spring we usually take the zero of PE to be when the spring is unstretched. When we give it an extension $x$ corresponding to tension $T$ it stores PE of $frac 12 Tx$.

So if we have two lifted-up bodies joined by a spring, the energy is the sum of 2 gravitational PE terms and 1 elastic PE term. This is because the PE 'belongs', in our analysis, to 3 systems: the Earth and $m_1$, the Earth and $m_2$, the parts of the spring.