To exercise the concept of potential energy and conservation
of mechanical energy consider the
following pendulum experiment. It is a good approximation to neglect
friction in this experiment and hence the
total mechanical energy is conserved.
The mechanical energy is
Where I choose the zero for potential energy to be when the pendulum
is at its lowest point. Conservation of 
allows us to calculate
the speed of the pendulum at its lowest point given the height at which
it was started out. All mechanical energy is potential at the high
point and kinetic at the low point hence
an expression we have seen many times before in the context of objects
in free fall.
Another amusing observation is that if I prevent the pendulum from
following its simple periodic motion by means of a non-dissipative force
it will nonetheless continue to reach the same
max height at the turning point where the kinetic energy vanishes
because that is required by the conservation of
mechanical energy.