Question

ignoring any friction, how is kinectic energy and potential energy related to each other as the ball swings back and forth ​

Answer 1

Im assuming this is a simple pendulum question.

Under no friction loss that means that we are not loosing any kinetic energy due to any friction between the string that is suspending the system, or wind resistance.

Under no friction loss the total mechanical energy is conserved. Meaning that the maximum amount of gravitational potential energy will be equal to the maximum kinetic energy of the pendulum.

The maximum kinetic energy will occur at the bottom of a pendulums motion, meaning that as the pendulum swings back and forth the place at which it makes a ninety degree angle relative to the surface of the ground or surface of whatever the pendulum is hanging under.

The maximum potential energy will be present when the pendulum ascends on either side at its maximum height, being at the two ends of the pendulums motion.

So:

ME is conserved under no friction meaning that

KEmax = PEmax

or

$\frac{1}{2} mv^{2}_{max} = mgh_{max}$

Hopefully this helps, I believe this is also an example of simple harmonic motion as well if thats what you are looking for!