a potential-energy diagram
One of the most powerful pictures in physics is a graph of an object's potential energy against its position — a potential-energy diagram. Read it like a landscape seen from the side: valleys are places of low potential energy, hills are places of high potential energy, and the object behaves much like a ball rolling on that very terrain.
You plot U (potential energy) up the page against position x across it. The force on the object is minus the slope of the curve, F = -dU/dx — in plain words, the force always points downhill on the graph, toward lower potential energy, and is strongest where the curve is steepest. The object's fixed total energy E is a horizontal line. Wherever that line sits above the curve, the gap E - U is the kinetic energy; where the line meets the curve, kinetic energy is zero and the object turns around — these are its turning points.
This lets you read a whole motion at a glance. A dip in the curve is a potential well that can trap the object, which then oscillates between two turning points; the bottom of a valley is a stable equilibrium, the top of a hill an unstable one. Physicists use these diagrams for everything from a mass on a spring (a simple parabola) to the bond between two atoms and the orbit of a planet.
For a mass on a spring, U = 1/2 k x^2 is an upward parabola centred at x = 0. Draw a horizontal line at the total energy E; the mass shuttles between the two points where the line cuts the parabola (its turning points), moving fastest at the bottom x = 0 where all the energy is kinetic, and stopping momentarily at the edges where all of it is potential.
The parabola is the spring's energy 'valley'; the flat line is the fixed total energy, and the object oscillates between where they cross.
The object is not literally rolling on the drawn curve — the curve is energy versus position, not a real hill. But the analogy is exact for the force: it always points toward lower potential energy, just as a ball rolls downhill.