mechanical energy
Watch a pendulum swing. At the bottom it is moving fastest — all motion. At the top of each swing it stops for an instant, poised highest — all height. Mechanical energy is the running total of these two: the energy an object has by virtue of its motion and its position combined.
It is simply the sum of kinetic and potential energy, E = K + U — one half m v squared plus whatever potential energy (gravitational, elastic) the object holds. As the pendulum swings, the two terms trade back and forth: kinetic energy grows as potential shrinks, and vice versa. Remarkably, if only conservative forces do work, their sum E stays exactly constant, even as each piece rises and falls.
Mechanical energy is the natural bookkeeping for pendulums, roller coasters, springs, and orbits — anywhere motion and position swap roles. But it is only the mechanical slice of a system's total energy; it ignores thermal, chemical, and other internal energy. That is why friction, which quietly bleeds mechanical energy into heat, makes the mechanical total shrink even though the grand total of all energy stays fixed.
A roller-coaster car at the top of a 30 m hill, momentarily at rest, has mechanical energy that is all potential: E = m g h. At the bottom, if the track is nearly frictionless, that same E is all kinetic, 1/2 m v^2 — so 1/2 v^2 = g h gives v = sqrt(2 g h) = sqrt(2 x 9.8 x 30) which is about 24 m/s, whatever the car's mass.
Height at the top becomes speed at the bottom, with the mechanical total unchanged along the way.
Mechanical energy is conserved only when nonconservative forces (like friction) do no work. In the real world it usually leaks away slowly as heat, which is why every real oscillation eventually dies down.