The above diagram plots various the energies involved
as a function of position (*x*) with *x*=0 being
the equilibrium (*F*=0) location. The
line representing "Total Energy" is flat, because total energy is
conserved (i.e., is constant). Potential energy
(*U(x)*) is plotted in red.
Total energy is the sum of
kinetic energy and potential energy: thus kinetic energy
is what you have to add to potential energy to get the
constant total energy. Kinetic energy must be positive,
so the only places the particle can actually go are where
*U(x)*<*E*. The points on the edge of
the allowed region (where *U(x)*=*E*, i.e.,
*x*=±*A*) are called turning
points. There the kinetic energy is zero, and so the velocity
of the particle is zero. Just prior to reaching *A*,
the particle is moving to the right (positive velocity, towards
positive *x*). Just after reaching
*A* the particle is moving to the left (negative
velocity, towards
negative *x*).
At *A* the particle is momentarily at rest.
The below plots the position and velocity as functions of time.